Derivación e Integración Numérica.ipynb

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      "source": [
        "<div align=\"center\">\n",
        "  <h1>Derivación e Integración Numérica</h1>\n",
        "  <p>\n",
        "    Autores:<br />\n",
        "    Sergio Andrés Majé Franco<br />\n",
        "    Marleny Rojas Gómez\n",
        "  </p> \n",
        "  <p>\n",
        "    Docente:<br />\n",
        "    Dr. Jesús Emilio Pinto Lopera \n",
        "  </p>\n",
        "  <p>\n",
        "    Universidad de la Amazonia<br />\n",
        "    Facultad de Ingeniería<br />\n",
        "    Programa Ingeniería de Sistemas<br />\n",
        "    Florencia - Caquetá<br />\n",
        "    2022\n",
        "  </p>\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-0NVvTzoh2pd"
      },
      "source": [
        "## Tabla de Contenido\n",
        "\n",
        "1. Introducción\n",
        "2. Desarrollo Metodológico\n",
        "    1. Desarrollo Teórico\n",
        "      1. Derivación Numérica\n",
        "      2. Integración con el método de Simpson 3/8\n",
        "    2. Desarrollo Computacional\n",
        "      1. Derivación\n",
        "      2. Integración\n",
        "3. Problemas\n",
        "  1. Problema para la derivación\n",
        "  2. Problema para la integral\n",
        "4. Resultados\n",
        "  1. Derivación\n",
        "  2. Integración\n",
        "5. Conclusiones\n",
        "6. Referencias"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x2rerzFlh8uM"
      },
      "source": [
        "## Tabla de Formulas\n",
        "\n",
        "1. Formula 1. Pendiente\n",
        "2. Formula 2. Derivación numérica\n",
        "3. Formula 3. Derivación numérica hacia adelante\n",
        "4. Formula 4. Derivación numérica hacia atras \n",
        "5. Formula 5. Derivación numérica central\n",
        "6. Formula 6. Regla de Simpson 3/8\n",
        "7. Formula 7. Reemplazar por h\n",
        "8. Formula 8. Integración - Hallar área bajo la curva"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "--etRs6oiCaY"
      },
      "source": [
        "## Tabla de Tablas\n",
        "\n",
        "1. Tabla 1. Derivación - Comparación\n",
        "2. Tabla 2. Integración - Resultados primera integral \n",
        "3. Tabla 3. Integración - Resultados segunda integral "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bDEvs_dmiHN9"
      },
      "source": [
        "## Tabla de Gráficos\n",
        "1. Figura 1. 3 formas de posibles arreglos\n",
        "2. Figura 2. Caso general\n",
        "3. Grafica 1. Derivación - Comparación funciones derivadas\n",
        "4. Grafica 2. Derivación - Funcion original\n",
        "5. Grafica 3. Derivación - Dos puntos\n",
        "6. Grafica 4. Integración - Área bajo la curva\n",
        "7. Grafica 5. Integración - Integral 1 - Área: Simpson 3/8\n",
        "8. Grafica 6. Integración Resultados primera integral\n",
        "9. Grafica 7. Integración - Integral 2 - Área: Simpson 3/8\n",
        "10. Grafica 8. Integración Resultados segunda integral\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2NMAcwWiiL2V"
      },
      "source": [
        "## 1. Introducción\n",
        "\n",
        "La derivación e integración numérica nos permite obtener variedad de herramientas fundamentales del cálculo, ayudándonos a modelar cualquier problema del mundo real y así obtener enfoques importantes al momento de encontrar una respectiva solución. Permite destacar diferentes alternativas, ventajas y preguntarnos por qué son tan importantes en nuestro día a día.\n",
        "\n",
        "El proceso que se va llevar a cabo para conocer a cerca de estas herramientas, lo vamos abarcar a través de unos métodos que compone cada una de ellas, para la derivada se va trabajar con el método de la pendiente y para la integral con el método de simpson 3/8. Permitiendo encontrar y comparar el procedimiento al momento de plasmarlo en una gráfica, dejándonos una enseñanza de acuerdo a su resultado.\n",
        "\n",
        "Con los conceptos, ejemplos, ejercicios y demás enfoques nos llevan a concluir una idea de lo profundo que puede llegar la derivada y la integral al representarla en todos los aspectos de la naturaleza, en las ciencias físicas relacionándolas con los métodos numéricos.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xVTYcQ0iiTha"
      },
      "source": [
        "## 2. Desarrollo Metodológico"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q8t-wMo_iYeZ"
      },
      "source": [
        "### 2.1. Desarrollo Teoríco"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OGn2VfLUi8O-"
      },
      "source": [
        "#### 2.1.1. Derivación Numérica"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0AQ-MvTzG2Eu"
      },
      "source": []
    },
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      "cell_type": "markdown",
      "metadata": {
        "id": "ALtCZDT80yzz"
      },
      "source": [
        "La derivada de una función, se interpreta como la pendiente de la curva de una respectiva función matemática f(x) la cual es trazada en función de x.\n",
        "\n",
        "Se debe tener en cuenta que la implicación de representar este modelo, conlleva mayo profundidad y ahí surge el por que es tan importante la derivada; muchas entidades físicas como la velocidad, aceleración, fuerza etc. Nos permiten tener un concepto claro sobre la tasa de cambio de otra cantidad. Con la derivada podemos dar un valor preciso para la tasa de cambio de tal manera que nos facilita modelar la cantidad esperada.\n",
        "\n",
        "$$ y = x \\cdot m + b $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 1. Pendiente\n",
        "</div>\n",
        "\n",
        "$$ \\frac{\\delta y}{\\delta x} = \\frac{y_2 - y_1}{x_2 - x_1} = m $$\n",
        "\n",
        "\n",
        "\n",
        "$$ \\frac{\\delta y}{\\delta x} = \\frac{f(x_2) - f(x_1)}{\\delta x} $$\n",
        "\n",
        "\n",
        "\n",
        "$$ \\frac{\\delta y}{\\delta x} = \\frac{f(x_1 + \\delta x) - f(x_2)}{\\delta x} $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 2. Derivación Numérica\n",
        "</div>\n",
        "\n",
        "\n",
        "\n",
        "Su resultado nos indica el comportamiento de la recta, si sale un valor de una pendiente positiva, la recta tiene esta inclinación “/”, si el valor es negativo se inclina hacia abajo, si es un valor = 0 es horizontal --- y si es infinito se representa de manera vertical.\n",
        "\n",
        "Supongamos que una función f(x) tiene su respectiva gráfica y al momento de llevarla al proceso de derivación saldrán muchas pendientes. Donde cada recta la toque un punto, para eso hay que darle un punto en específico y saber la pendiente que deseamos observar. De acuerdo a su referencia sabemos cuál sería su posición y su valor, con ayuda de las pendientes podemos ir sustituyendo valores de puntos en la ecuación de la derivada, saber si está subiendo o bajando.\n",
        "Lo importante que se puede destacar de las pendientes en una recta, es el analizar el comportamiento de las curvas.\n",
        "\n",
        "$$ \\frac{d}{dx}\\ f(x_{\\left[i\\right]})=  \\frac{\\ f(x_{\\left[i+1\\right]})-  f(x_{\\left[i\\right]})}{∆x} $$\n",
        "\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 3. Derivación numérica hacia adelante\n",
        "</div>\n",
        "\n",
        "\n",
        "\n",
        "$$ \\frac{d}{dx}\\ f(x_{\\left[i\\right]})=  \\frac{\\ f(x_{\\left[i\\right]})-  f(x_{\\left[i-1\\right]})}{∆x} $$\n",
        "\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 4. Derivación numérica hacia atrás\n",
        "</div>\n",
        "\n",
        "$$ \\frac{d}{dx}\\ f\\ \\left(x_{\\left[i\\right]}\\right) = \\frac{\\ f(x_{\\left[i+1\\right]})-  f(x_{\\left[i-1\\right]})}{2∆x} $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 5. Derivación numérica central\n",
        "</div>\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nduUU11Sjyvo"
      },
      "source": [
        "#### 2.1.2. Integración con el método de Simpson 3/8"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m7XgQnkTsjTQ"
      },
      "source": [
        "\n",
        "La integral de una función, la podemos comprender geográficamente como el área bajo la curva de una función f(x) trazada como una función de x.\n",
        "\n",
        "Por lo tanto, la integral nos facilita de diferentes formas de representar un numero infinito y así conseguir una expresión analítica del área bajo la curva, muchas de las definiciones de entidades físicas convierten su forma de manera matemática, desglosándola de un área bajo una curva. Un ejemplo claro es el encontrar la masa de un cuerpo, interviene diferentes elementos de masa y que al realizar la operación de multiplicación por la distancia a un eje de rotación, nos deduce un proceso para encontrar el valor preciso y ahí es donde se necesita de la integral, es donde damos respuesta del por que es necesaria, la integral es una herramientas sumamente primordial para dar soluciones a sumas infinitas.\n",
        "\n",
        "\n",
        "Uso del metodo simpson 3/8 en la integral\n",
        "\n",
        "Se usa para tener valores más aproximados y precisos de integrales definidos, representa un método numérico para cálculos deduciéndolo por medio de la regla de Simpson la cual es:\n",
        "F(x) : Integrand\n",
        "A : Límite inferior de integración \n",
        "B : Límite superior de integración\n",
        "Existen dos tipo de reglas Simpson, 1/3 y 3/8 para este caso vamos implementar la de 3/8, el interpolante es un polinomio cubico, utiliza un valor de función mas y se aproxima dos veces de manera mas precisa.\n",
        "\n",
        "\n",
        "$$ \\int_{a}^{b}f(x)\\ dx\\ \\approx\\ \\frac{b-a}{8}\\ \\left\\{f(a)\\ +\\ 3f\\ (\\frac{2a\\ +\\ b}{3}\\ +\\ 3f\\ (\\frac{a\\ +\\ 2b}{3}\\ )+\\ f(b)\\left.\\right\\}\\right. $$\n",
        "\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 6. Regla de Simpson 3/8\n",
        "</div>\n",
        "\n",
        "\n",
        "Procedemos a tomar el valor correspondiente a (b-a)/3 de la formula anterior y la reemplazamos como h, y quedaría de la siguiente manera:\n",
        "\n",
        "\n",
        "$$\\int_{a}^{b}f(x)\\ dx\\approx\\frac{3h}{8}\\ \\left\\{f(a)\\ +\\ 3f\\ (\\frac{2a\\ +\\ b}{3})\\ +\\ 3f\\ (\\frac{a\\ +\\ 2b}{3})\\ +\\ f(b)\\left.\\right\\}\\right.\\ $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 7. Reemplazar por h\n",
        "</div>\n",
        "\n",
        "La presente regla de 3/8 para n intervalos, lo que nos quiere decir es que n debería ser un múltiplo de 3 quedando así:\n",
        "\n",
        "$$\\int_{a}^{b}{f(x)\\ dx\\ \\approx\\ \\frac{3h}{8}\\ \\sum_{j=1}^{n/3}\\left\\{f\\ (x_{3j-3})\\ +\\ 3f\\ (x_{3j-2})\\ +\\ 3f\\ (x_{3j-1})\\ +\\ f(x_{3j})\\left.\\right\\}\\right.}$$\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aGnpKKrWikL0"
      },
      "source": [
        "### 2.2. Desarrollo Computacional"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z0tHDpl4uKcd"
      },
      "source": [
        "Para el desarrollo de computacional relacionado a este informe se uso el lenguaje de programación Python 3.10.7 y las siguientes librerías:\n",
        "\n",
        "* timeit - librería especializada en el manejo del tiempo con mayor precisión.\n",
        "* matplotlib - permite graficar los resultados de los procesos.\n",
        "* numpy - se especializa en el cálculo, transformación y análisis de datos numéricos.\n",
        "* pandas - permite la manipulación y análisis de datos sobre tablas numéricas y series temporales."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "Yve5vLXc7R22"
      },
      "outputs": [],
      "source": [
        "from timeit import default_timer as timer\n",
        "from typing import Callable\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jaXWPyK4uixd"
      },
      "source": [
        "Para medir el tiempo transcurrido de los algoritmos y funciones que se implementan en este informe se empleo la función decorador ```count_elapsed_time()```."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "CPQ-TOEz__cH"
      },
      "outputs": [],
      "source": [
        "def count_elapsed_time(func):\n",
        "    '''\n",
        "    Decorador.\n",
        "    Ejecuta la función y calcula el tiempo transcurrido.\n",
        "    Retorna el resultado de la función y el tiempo transcurrido.\n",
        "    '''\n",
        "    def wrapper(*args, **kwargs):\n",
        "        start_time = timer()\n",
        "        ret = func(*args, **kwargs)\n",
        "        elapsed_time = timer() - start_time\n",
        "        return (elapsed_time, *ret)\n",
        "\n",
        "    return wrapper"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G15b4dInkJrM"
      },
      "source": [
        "#### 2.2.1. Derivación"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0IIZ8q06uoQN"
      },
      "source": [
        "El método ```derivate``` proveé una solución aproximada mediante diferenciación numérica"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "qcIVLb_eRZIu"
      },
      "outputs": [],
      "source": [
        "@count_elapsed_time\n",
        "def derivative(\n",
        "  f: Callable[[float], float],\n",
        "  x0: int,\n",
        "  dx: float = 1e-15\n",
        ") -> float:\n",
        "  '''Da una solución aproximada a un punto de la derivada\n",
        "\n",
        "  Args:\n",
        "    f: función a derivar\n",
        "    x0: punto a dar una solución aproximada en la función derivada\n",
        "    dx: delta de x\n",
        "  '''\n",
        "  return ((f(x0 + dx) - f(x0)) / dx, 0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EyprsAnwvwTT"
      },
      "source": [
        "El método ```derivative_points``` devuelve todo los puntos de inflexión que se hayan entre dos puntos en específicos de la función derivada."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "dtRtR3AXSDMQ"
      },
      "outputs": [],
      "source": [
        "@count_elapsed_time\n",
        "def derivative_points(\n",
        "    f: Callable[[float], float],\n",
        "    x0: int,\n",
        "    xn: int,\n",
        "    n: int\n",
        "):\n",
        "  '''Puntos de inflexión entre dos puntos en específico de la función\n",
        "  dada a derivar.\n",
        "\n",
        "  Args:\n",
        "    f: función a derivar\n",
        "    x0: punto inicial de corte\n",
        "    xn: punto final de corte\n",
        "    n: cantidad de datos (puntos) de aproximación \n",
        "  '''\n",
        "  x = np.linspace(x0, xn, n)\n",
        "  dx = (xn - x0) / (n - 1)\n",
        "\n",
        "  y = f(x)\n",
        "  yp = np.zeros_like(x)\n",
        "\n",
        "  for i in range(n):\n",
        "      if i == 0:\n",
        "          yp[i] = (y[i + 1] - y[i]) / dx\n",
        "      elif i == n - 1:\n",
        "          yp[i] = (y[i] - y[i - 1]) / dx\n",
        "      else:\n",
        "          yp[i] = (y[i + 1] - y[i - 1]) / (2 * dx)\n",
        "\n",
        "  return yp"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "itzdgSOAkSPU"
      },
      "source": [
        "#### 2.2.2 Integración"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wWF1lpA7wyCr"
      },
      "source": [
        "El método ```integration``` proveé una solución aproximada para una función a integrar, usando el método **Simpson $\\frac{3}{8}$**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "dpd3200s69Xe"
      },
      "outputs": [],
      "source": [
        "@count_elapsed_time\n",
        "def integration(\n",
        "  f: Callable[[float], float],\n",
        "  x0: int,\n",
        "  xn: int,\n",
        "  error: float = 0.002,\n",
        "  table: list = None\n",
        ") -> float:\n",
        "  '''Da un resultado aproximado para una integral definida.\n",
        "\n",
        "  Args:\n",
        "    f: función a integrar\n",
        "    x0: Definición a de la integral\n",
        "    xn: Definición b de la integral\n",
        "    error: Error tolerado en la aproximación\n",
        "    table: tabla para datos\n",
        "\n",
        "  Returns:\n",
        "    result: Resultado aproximado de la integral definida\n",
        "    table: Tabla con los datos de operación del método\n",
        "  '''\n",
        "  n = 0\n",
        "  e = 1\n",
        "  result = None\n",
        "  table = []\n",
        "\n",
        "  while e > error:\n",
        "    n += 3\n",
        "    h = (xn - x0) / n\n",
        "    x = np.linspace(0, n, n + 1) * h + x0\n",
        "    fv = np.vectorize(f)\n",
        "    result = (\n",
        "        3 * h / 8 * (\n",
        "            f(x[0]) +\n",
        "            3 * fv(x[np.mod(np.arange(len(x)), 3) != 0]).sum() +  # Salta todos los 3° indices\n",
        "            2 * fv(x[::3]).sum() +  # Obtiene todos los 3° indices\n",
        "            f(x[-1])\n",
        "        )\n",
        "    )\n",
        "    e = np.abs(((-3 * h ** 5) / 80) * result ** 4 * np.mean([xn, x0]))\n",
        "\n",
        "    table.append([n, h, result, e])\n",
        "\n",
        "  return result, table"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X5Xvxw0usyOf"
      },
      "source": [
        "## 3. Problemas"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o1npia2qs6WN"
      },
      "source": [
        "### 3.1. Problema para la derivación\n",
        "\n",
        "Un agricultor tiene 2400 pies de material y quiere construir una barda para\n",
        "cercar un campo rectangular que bordea un río recto, de modo que no necesita barda a\n",
        "lo largo del río. ¿Cuáles son las dimensiones que debe tener el campo para encerrar el\n",
        "área más grande? \n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "<div align=\"center\">\n",
        "    Figura 1. 3 formas de posibles arreglos\n",
        "</div>\n",
        "\n",
        "Vemos que cuando intentamos campos muy anchos y poco largos, o campos angostos\n",
        "y muy largos, obtenemos áreas relativamente pequeñas. Parece verosímil que exista\n",
        "alguna configuración intermedia que produzca el área más grande.\n",
        "\n",
        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)\n",
        "\n",
        "\n",
        "<div align=\"center\">\n",
        "    Figura 2. Caso General\n",
        "</div>\n",
        "\n",
        "Queremos maximizar el área A del rectángulo. Sea\n",
        "x y y el largo y el ancho, respectivamente, del rectángulo (en pies). Entonces, queremos\n",
        "expresar A en términos de x y y:\n",
        "\n",
        "$$  A = xy $$\n",
        "\n",
        "Queremos expresar A en función de una sola variable, por lo que eliminamos y\n",
        "expresándola en términos de x. Para ello utilizamos la información dada de que la\n",
        "longitud total de la barda es 2 400 pies. \n",
        "Quedando así: \n",
        "\n",
        "$$ 2x + y = 2400 $$\n",
        "\n",
        "De esta ecuación tenemos y = 2400 + 2x, por lo tanto:\n",
        "\n",
        "$$ A = x(2400-2x) = 2400x - 2x^2$$\n",
        "\n",
        "\n",
        "Tener claro que, $x\\geq0$ y  $x\\le1200$ (de lo contrario $A < 0$), así que la función que deseamos maximizar es:\n",
        "\n",
        "$$A(x) = 2400 - 2x^2 \\hspace{1cm}  0 \\le x \\le 1200$$\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RKZtRS-otLS_"
      },
      "source": [
        "### 3.2. Problema para la Integral\n",
        "\n",
        "El problema que vamos abordar para la integral es el siguiente: \n",
        "Determinar la longitud de arco de una curva. \n",
        "\n",
        "Según la funcion:  $ y = x^3 - 6x^2 + 8x$ y el eje $x$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3e55JXrLinZf"
      },
      "source": [
        "## 4. Resultados"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wxXykml5RHG1"
      },
      "source": [
        "### 4.1. Derivación"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J52uY0Q-ytX7"
      },
      "source": [
        "La derivada es $A´(x) = 2 400 - 4x$, así que para encontrar los números críticos\n",
        "resolvemos\n",
        "\n",
        "$$ 2 400 - 4x = 0$$\n",
        "\n",
        "que da $x = 600$. El valor máximo de A debe producirse en este número crítico o en un\n",
        "extremo del intervalo. Ya que $A(0) = 0$, $A(600) = 720 000$ y $A(1200) = 0$, el método del intervalo cerrado da el valor máximo cuando $A(600) = 720 000$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "iDWqqDUpWcYy"
      },
      "outputs": [],
      "source": [
        "f: Callable[[float], float] = lambda x: 2400 * x - 2 * x ** 2  # Función a derivar\n",
        "fp: Callable[[float], float] = lambda x: 2400 - 4 * x  # Función derivada"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "2EXs3ImlWMSO"
      },
      "outputs": [],
      "source": [
        "time, result, _ = derivative(f, 600)\n",
        "time_points, *points = derivative_points(f, 0, 1200, 30)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jrPCiGtkXdF-",
        "outputId": "c5078f63-046a-4b3c-c0b8-832cc3c409e0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "El resultado de la derivada es 0.0, en un tiempo de 1.091699959943071e-05 segundos\n",
            "El resultado de la derivada analítica es 0\n",
            "El error de la aproximación de la derivación numérica es de 0.0\n",
            "Los puntos de corte en el eje x y y tuvo un tiempo de 0.00045464199865818955 segundos\n"
          ]
        }
      ],
      "source": [
        "print(f'El resultado de la derivada es {result}, en un tiempo de {time} segundos')\n",
        "print(f'El resultado de la derivada analítica es {fp(600)}')\n",
        "print(f'El error de la aproximación de la derivación numérica es de {np.abs(fp(600) - result)}')\n",
        "print(f'Los puntos de corte en el eje x y y tuvo un tiempo de {time_points} segundos')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 990
        },
        "id": "4gLfYY3lYVVc",
        "outputId": "c0baf480-b7c2-4944-b8b6-2f3641b7c50c"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-b5302053-3153-488f-8bcf-9276780132bc\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Points</th>\n",
              "      <th>f´(x)</th>\n",
              "      <th>Error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2317.241379</td>\n",
              "      <td>2400.000000</td>\n",
              "      <td>8.275862e+01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2234.482759</td>\n",
              "      <td>2234.482759</td>\n",
              "      <td>4.547474e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2068.965517</td>\n",
              "      <td>2068.965517</td>\n",
              "      <td>4.547474e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1903.448276</td>\n",
              "      <td>1903.448276</td>\n",
              "      <td>2.273737e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1737.931034</td>\n",
              "      <td>1737.931034</td>\n",
              "      <td>9.094947e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1572.413793</td>\n",
              "      <td>1572.413793</td>\n",
              "      <td>2.273737e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1406.896552</td>\n",
              "      <td>1406.896552</td>\n",
              "      <td>4.547474e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1241.379310</td>\n",
              "      <td>1241.379310</td>\n",
              "      <td>2.273737e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1075.862069</td>\n",
              "      <td>1075.862069</td>\n",
              "      <td>6.821210e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>910.344828</td>\n",
              "      <td>910.344828</td>\n",
              "      <td>1.136868e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>744.827586</td>\n",
              "      <td>744.827586</td>\n",
              "      <td>6.821210e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>579.310345</td>\n",
              "      <td>579.310345</td>\n",
              "      <td>0.000000e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>413.793103</td>\n",
              "      <td>413.793103</td>\n",
              "      <td>5.684342e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>248.275862</td>\n",
              "      <td>248.275862</td>\n",
              "      <td>3.126388e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>82.758621</td>\n",
              "      <td>82.758621</td>\n",
              "      <td>7.389644e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>-82.758621</td>\n",
              "      <td>-82.758621</td>\n",
              "      <td>2.131628e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>-248.275862</td>\n",
              "      <td>-248.275862</td>\n",
              "      <td>1.733724e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>-413.793103</td>\n",
              "      <td>-413.793103</td>\n",
              "      <td>2.273737e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>-579.310345</td>\n",
              "      <td>-579.310345</td>\n",
              "      <td>1.477929e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>-744.827586</td>\n",
              "      <td>-744.827586</td>\n",
              "      <td>4.547474e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>-910.344828</td>\n",
              "      <td>-910.344828</td>\n",
              "      <td>1.477929e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>-1075.862069</td>\n",
              "      <td>-1075.862069</td>\n",
              "      <td>2.273737e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>-1241.379310</td>\n",
              "      <td>-1241.379310</td>\n",
              "      <td>2.273737e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>-1406.896552</td>\n",
              "      <td>-1406.896552</td>\n",
              "      <td>6.821210e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>-1572.413793</td>\n",
              "      <td>-1572.413793</td>\n",
              "      <td>1.364242e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>-1737.931034</td>\n",
              "      <td>-1737.931034</td>\n",
              "      <td>3.637979e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>-1903.448276</td>\n",
              "      <td>-1903.448276</td>\n",
              "      <td>4.547474e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>-2068.965517</td>\n",
              "      <td>-2068.965517</td>\n",
              "      <td>6.366463e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>-2234.482759</td>\n",
              "      <td>-2234.482759</td>\n",
              "      <td>1.364242e-12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>-2317.241379</td>\n",
              "      <td>-2400.000000</td>\n",
              "      <td>8.275862e+01</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b5302053-3153-488f-8bcf-9276780132bc')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-b5302053-3153-488f-8bcf-9276780132bc button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b5302053-3153-488f-8bcf-9276780132bc');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "         Points        f´(x)         Error\n",
              "0   2317.241379  2400.000000  8.275862e+01\n",
              "1   2234.482759  2234.482759  4.547474e-13\n",
              "2   2068.965517  2068.965517  4.547474e-13\n",
              "3   1903.448276  1903.448276  2.273737e-13\n",
              "4   1737.931034  1737.931034  9.094947e-13\n",
              "5   1572.413793  1572.413793  2.273737e-13\n",
              "6   1406.896552  1406.896552  4.547474e-13\n",
              "7   1241.379310  1241.379310  2.273737e-13\n",
              "8   1075.862069  1075.862069  6.821210e-13\n",
              "9    910.344828   910.344828  1.136868e-13\n",
              "10   744.827586   744.827586  6.821210e-13\n",
              "11   579.310345   579.310345  0.000000e+00\n",
              "12   413.793103   413.793103  5.684342e-13\n",
              "13   248.275862   248.275862  3.126388e-13\n",
              "14    82.758621    82.758621  7.389644e-13\n",
              "15   -82.758621   -82.758621  2.131628e-13\n",
              "16  -248.275862  -248.275862  1.733724e-12\n",
              "17  -413.793103  -413.793103  2.273737e-12\n",
              "18  -579.310345  -579.310345  1.477929e-12\n",
              "19  -744.827586  -744.827586  4.547474e-13\n",
              "20  -910.344828  -910.344828  1.477929e-12\n",
              "21 -1075.862069 -1075.862069  2.273737e-12\n",
              "22 -1241.379310 -1241.379310  2.273737e-13\n",
              "23 -1406.896552 -1406.896552  6.821210e-13\n",
              "24 -1572.413793 -1572.413793  1.364242e-12\n",
              "25 -1737.931034 -1737.931034  3.637979e-12\n",
              "26 -1903.448276 -1903.448276  4.547474e-13\n",
              "27 -2068.965517 -2068.965517  6.366463e-12\n",
              "28 -2234.482759 -2234.482759  1.364242e-12\n",
              "29 -2317.241379 -2400.000000  8.275862e+01"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = np.linspace(0, 1200, 30)\n",
        "fx = f(x)\n",
        "fpx = fp(x)\n",
        "\n",
        "pd.DataFrame(\n",
        "  list(map(lambda point: [point[0], point[1], np.abs(point[1] - point[0])], zip(points, fpx))),\n",
        "  columns=['Points', 'f´(x)', 'Error']\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BrTgUC4TzeMd"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 1. Derivación - Comparación\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 567
        },
        "id": "NoHpbAUfcL85",
        "outputId": "d6e54a83-cdeb-4349-f9a9-9428f22d2a64"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1008x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(14, 9))\n",
        "\n",
        "plt.plot(x, fpx, label='f´(x)')\n",
        "plt.plot(x, points, label='y´')\n",
        "\n",
        "plt.axvline(600, color='r')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Derivación numérica')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AJOQVWM6zr2C"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 1. Derivación - Comparación funciones derivadas\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 567
        },
        "id": "hPauM1bIq3PS",
        "outputId": "0674dff0-8d2e-443b-9e15-5d89755401ee"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1008x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(14, 9))\n",
        "\n",
        "plt.plot(x, fx, label='f(x)')\n",
        "\n",
        "plt.axvline(600, color='r')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Derivación numérica')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-UFpsdsgz0PL"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 2. Derivadas - Función original\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 330
        },
        "id": "JnQB1R3Tj-Xr",
        "outputId": "9e4ebe2f-ebc6-4e4e-c166-b092117a8936"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "x0: 100\n",
            "xn: 2000\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x0 = next(map(int, input('x0: ').split()))\n",
        "xn = next(map(int, input('xn: ').split()))\n",
        "\n",
        "if x0 > xn:\n",
        "  raise 'xn no puede ser mayor a x0'\n",
        "\n",
        "_, *two_points = derivative_points(f, x0, xn, 30)\n",
        "xi = np.linspace(x0, xn, 30)\n",
        "\n",
        "plt.plot(xi, two_points, label='y´')\n",
        "plt.plot(xi, two_points, 'o')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Derivación numérica - dos puntos')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hYcw9CkZz_ka"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 3. Derivación - dos puntos\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gTOmDWIcBW34"
      },
      "source": [
        "### 4.2 Integración"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "_vP4kh0ZBWN0"
      },
      "outputs": [],
      "source": [
        "f: Callable[[float], float] = lambda x: x ** 3 - 6 * x ** 2 + 8 * x  # función a integrar"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "o-wSjvjmBs3l",
        "outputId": "fe4bb18e-c4d4-45fd-a268-e5f8ecf5266a"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = list(range(10))\n",
        "\n",
        "plt.plot(x, [f(i) for i in x], linewidth=2)\n",
        "plt.plot(x, [f(i) for i in x], 'o', linewidth=2)\n",
        "\n",
        "plt.fill_between(x, [f(i) for i in x], color='yellow')\n",
        "\n",
        "plt.axhline(0, color=\"black\")\n",
        "plt.axvline(0, color=\"black\")\n",
        "\n",
        "plt.xlim(0, 10)\n",
        "plt.ylim(-5, 5)\n",
        "\n",
        "plt.title('Curva')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('f(x)')\n",
        "plt.grid()\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1Eeofa0T0Mt3"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 4. Integración - Área bajo la curva\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ePepclkPHJs_"
      },
      "source": [
        "Entendiendo los espacios amarillos de la gráfica como el área de la curva y teniendo en cuenta que la curva corta al eje $x$ en $0$, $2$ y $4$, nos disponemos a hallar el valor del área mediante el uso de integrales.\n",
        "\n",
        "$$A = \\int_0^2 (x^3 - 6x^2 + 8) \\,dx - \\int_2^4 (x^3 - 6x^2 + 8) \\,dx $$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x6QBwVI40TaA"
      },
      "source": [
        "<div align=\"center\">\n",
        "\n",
        "    Formula 8. Integración - Hallar área bajo la curva\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I-QDAJJMJCAn",
        "outputId": "198faed8-4768-4f50-db56-48a0a50761e7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "8.0"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "time1, a1, table1 = integration(f, 0, 2)\n",
        "time2, a2, table2 = integration(f, 2, 4)\n",
        "\n",
        "A = a1 - a2\n",
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9FRdh8jWLwlM",
        "outputId": "67d75b65-0337-4cbd-b25b-758141a86cfe"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "La primera integral obtuvo un resultado de 4.0, en un tiempo de 0.0017219000001205131 segundos\n",
            "La segunda integral obtuvo un resultado de -4.0, en un tiempo de 0.001368102999549592 segundos\n",
            "El área total de bajo la curva dada es de 8.0u^2\n"
          ]
        }
      ],
      "source": [
        "print(f'La primera integral obtuvo un resultado de {a1}, en un tiempo de {time1} segundos')\n",
        "print(f'La segunda integral obtuvo un resultado de {a2}, en un tiempo de {time2} segundos')\n",
        "print(f'El área total de bajo la curva dada es de {A}u^2')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VtZfQkG01CCX"
      },
      "source": [
        "Primer integrada"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "H0_skdAnMzUP",
        "outputId": "9f43a735-0e4a-4ea0-c2d4-d5e4ae0b7f28"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-277355b2-3175-445d-8abd-3dbd98fb01ce\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>Intervalo</th>\n",
              "      <th>Resultado</th>\n",
              "      <th>Error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>3.0</td>\n",
              "      <td>0.666667</td>\n",
              "      <td>4.0</td>\n",
              "      <td>1.264198</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>6.0</td>\n",
              "      <td>0.333333</td>\n",
              "      <td>4.0</td>\n",
              "      <td>0.039506</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>9.0</td>\n",
              "      <td>0.222222</td>\n",
              "      <td>4.0</td>\n",
              "      <td>0.005202</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>12.0</td>\n",
              "      <td>0.166667</td>\n",
              "      <td>4.0</td>\n",
              "      <td>0.001235</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-277355b2-3175-445d-8abd-3dbd98fb01ce')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-277355b2-3175-445d-8abd-3dbd98fb01ce button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-277355b2-3175-445d-8abd-3dbd98fb01ce');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "      n  Intervalo  Resultado     Error\n",
              "0   3.0   0.666667        4.0  1.264198\n",
              "1   6.0   0.333333        4.0  0.039506\n",
              "2   9.0   0.222222        4.0  0.005202\n",
              "3  12.0   0.166667        4.0  0.001235"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table1), columns=['n', 'Intervalo', 'Resultado', 'Error'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1DgwRTnY0dYf"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 2. Integración - Resultados primer integral\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "w8zxunaigdKO",
        "outputId": "ff29828c-df95-4de8-d39d-80213d8c2e9a"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "WARNING:matplotlib.legend:No handles with labels found to put in legend.\n"
          ]
        },
        {
          "data": {
            "image/png": 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HOz+Yy8rt+3nmuiHccu5oZ0Ilj/Gv7k5osJ33bx/AuMUXMnDUvVz75gxuO68BD19xDnUTK96JiDHBZlsExlOLMrO45vUZZO7Zzfu3P/NzEYhSItC70wy++0t/fnveGD6evZvLXkxjTMamKl0jxphgsEJgPDNhyTZuHDyTuNjtDP/9o1xy8uzyF4oSdRMP8eQ1bzHyvr/QuE4m93+awR0fTGDTnkN+RzNRyAqBCTpV5Z1pa7n3k/mcnLKWEfc/xClNV/odKyydccIqvr7/TwzoO4S56w5w+cvf8ubkRRQUFZe/sDFBYoXABFVhUTH/+HoxT49ZRq/Tv2dov4dpUmeH37HCWo3YYu68aBTf/aU/3U+ey/PfbKTPa6OZt97OrTShYYXABM2B3ALu+nAen8zeyL3dRvLGb56iZnxkHQ7qpWbJu3nrtmd493dPcjBvL9e/NZtHv5zGvkP55S9szHGwo4ZMUGzel8NdH8xl9Y4snvvlEG7umuZ3pGqr52lzOb9tf1757hbenX4NE5aO5fHeZ/DLuLnIxEGQlQnJ1ueBCR4rBOa4ZWTu464P55JbkM0Hd/yLi9rP8TtStVcrPo+/936P686axN9HPMiUL+fQN+EdEtTdOrA+D0wQWdOQOS7fLN7GjYNnkVBjO1/9/hErAkF2WrP1fNn/Lzxb992fi8Bhh/s8MOY42RaBqRJV5e1pa3lu3HLOaLmWt3/7FI3rHN1bkjl+MTFKUm4uUEoPPGVcvM+YyrBCYCqtoKiYJ0Yt4dM5G+nTaTYv3vhvEuPy/I4V2ZLV6W6zBE1uWVp5MKZSrGnIVMr+3ALu/GAun87ZyH3dv+I/Nz9jRSAUeuY6F+ULcEjjGdHgOjsj2Rw3KwSmwjbtOcT1/53JrDU7eP76N/hbr/eIibEvoZAI6PMAFE0uZlybs3lo2XkM+PobiovtfTBVZ01DpkIWbNrH3R/OJb/wAB/d+U8uaDfX70jRJ+AifQL8Uiew8pvmDJ5yPQVF43j2uiuJibGGIlN5VghM6TKGwcRBdMvKJGdOMz7Ovo6adU5jaL8naddkjd/pDM4F7B7t9QEJsQW8Nulm8ovS+Pf1fYm1YmAqyQqBOVpAx/IC1MzZwjOxQyjoXkSdJvv8TmcCiMBDv/gfcbGFvPjtbRQUjeKlG68izjq9MZVgnxZztFI6lk+kgDozIq/TmEjxQM/PeezK9xi9sAYPfDqK/EK7aJ2pOCsE5mhlHZteyuGLJnzc2+0rBvQdwjdL4vj9JyPJLSjyO5KpJqwQmKPkJzUvfUJ17Vg+itx50SievvYNJi5P4J6PrBiYirFCYI5QUFTMK8U3kUP8kRMisGP5SHXreeN4/levMn11PHe8/xWH8q1JzxybFQJzhDfSV/Pmns6s7NoMkotRiOiO5SPVjed8y0s3vsScdYnc/t5X5BTa1pwpmx01ZH6yeHMWr09axbVnTuOM3ougN0yZ/ALduz/sdzRTBdedNZm42EL+OPSv7N67nwsuLCC5ZpzfsUwY8myLQEROEJF0EVkqIktE5I+lzNNdRLJEZIE7DPAqjzm2/MJiHv5iIfVrZzPw6sF+xzFB0jd1Om/e8hzr98dy6ztfse+QXQ7EHM3LpqFC4C+q2gE4D7hfRDqUMt80VT3THeyauj75z6RVLN92gOeue4N6texcgUhyxemzeeCsTFZsj+fmt0ewO9v29ZgjeVYIVHWrqv7g3j4ALANaePV8puoyMvfx5uTV/OrsyVzWYZrfcYwHzmxykHd++xRrdyZw05CR7DhgxcD8TEJx5UIRaQ1MBTqq6v6A8d2BL4FMYAvwsKouKWX5fkA/gJSUlM5Dhw6tUo7s7GySkpKqtKyX/MxVUKw8MTOHQwWFPHPRWmrHHXm4YXZ2S5KSwu+a95arcg7nWra7Fq/80JL6CcU80rUO9RP9PV7E/icr53hy9ejRY76qdil1oqp6OgBJwHzgl6VMqwskubd7A6vKe7zOnTtrVaWnp1d5WS/5meuf45Zpq0fSdNLyC7S0VZ6e/kKp4/0eLFfVc81dd5qePmCYXvL8Z5q5N1v9ZP+TlXM8uYB5WsYHxNOfAyISh/OL/3+q+lUpRWi/qma7t8cCcSLSyMtM5mc/btzL4Clr+HWXSfQ4ZabfcUyIdGm9jI/v+j/2HIzhxrfS2Lj7gN+RjM+8PGpIgHeBZar6UhnzNHXnQ0S6unl2e5XJ/Cy3oIiHv1hI07pZPN73bb/jmBA768SVfHbP3zmYr/x6yFjW7cryO5LxkZdbBBcCtwGXBhwe2ltE+otIf3ee64HFIrIQeA24yd2EMR576duVrNl5kH9d/xp1E+0XYTTq2GINn93zGPmFRdw4eDyrtu/xO5LxiZdHDU1XVVHVVP358NCxqvqWqr7lzvO6qp6uqmeo6nmqau0TITB/wx7enraW35z7LRe3n+N3HOOj05qtZ2i/R4F8bhoykWVbd/kdyfjALjERZXLynSahFvX28vfe7/gdx4SB9imb+LzfI8TF5vDR4OfIf+E0GFgPXu7o9E1hIp5dYiLK/Hv8CtbtOsSn97xGUsJBv+OYMHFS4y2kdX+I2hMgPrvAGZm1yemgCCD1Rv/CGc/ZFkEUmbN2N+/PXMfvzh/HBW2tz2FzpEZz8qhJwZEjC3KcjopMRLNCECUO5Rfy1+ELOaH+Hh658j2/45hwVFbHQ2V1VGQihhWCKPGvccvZtPcQL9zwCrXic8pfwESfMjoe0uSWIQ5iQs0KQRSYuWYXH87awB0XjKFrmx/8jmPCVc9cpwOiAIc0nnFNrvIpkAkVKwQRLjuvkL8Nz6BNo1389YoP/I5jwllqodMBUXIxoGhyMSNansd9iy7i26U/+p3OeMiOGopwz41dxuZ9hxje/xVqxtsVJ005UgshNRsAAX5VMJ7PB/fkz5/nMPL+5rRrkuJvPuMJ2yKIYNNW7eR/czZyz8Wj6dxqgd9xTDWUGFfAW7c+Q0KNfO79eAIHcvP9jmQ8YIUgQh3ILeCR4Rm0bbyDhy7/0O84phprXm8Xr//mn6zfncxDw76guNiuAhNprBBEqGfGLGPb/hxeuOEVEuOse0JzfM5vu4jHe7/Lt0vr8Xr6OL/jmCCzQhCBJq/YwdC5m7i320jOOjHD7zgmQtxx4SiuO2sSL39XxMRlC/2OY4LICkGEycop4NEvMzg5ZSt/usyahEzwiMCz171Bh2br+NPQVazducPvSCZIrBBEmKfSlrIzO5cXbniVhBqFfscxEaZmfB6Db3uaGrEF3PvxeLLzCspfyIQ9KwQRZOKy7Qyfn8l93b8kteViv+OYCNWy/k7e+M0/WbOzHg8PG4Z1IVL9WSGIEPsO5fPYVxmc2nQzD1z6id9xTIS7oF0Gf+/9Ht8sqcebk7/xO445TlYIIsSTo5ey56DTJBRvTUImBO66aCRXnzGZFyYUkr7CDkqozqwQRIDxS7Yx4sfN/OHSL+jYYqnfcUyUEIF//eo/nNp0PX/8bAXrd+30O5KpIisE1dyeg/k8PmIRHZplcn+PT/2OY6JMzfg8htz2DDExRdz78TcctJ3H1ZIVgmruiVFLyMrJ5cUbXyYutsjvOCYKndBgO/+5+V+s2lGPvw3/wnYeV0NWCKqxsYu2MnrhFv7Y83NOa7bC7zgmil3cfgF/6/UhYxYlM3jqBL/jmEqyq49WNxnDYOIgNCuTM2nIHxpeSv9un/mdyhjuveRLFm1uy/PfXESHZou55OSOfkcyFWRbBNVJxjCnM/GsTQhKc3bxUN4waiyxt9H4TwT+ff2rnJyykQc+W8rG3bv9jmQqyLNvEBE5QUTSRWSpiCwRkT+WMo+IyGsislpEMkTkbK/yRISJg5zOxAPEFAITE/3JY0wJtdwzj1WVfh+P5VC+7TyuDrz8KVkI/EVVOwDnAfeLSIcS81wJtHeHfsB/PcxT/ZXViXhZnY4b44NWDbfx2s3Ps2J7PR75crjtPK4GPCsEqrpVVX9wbx8AlgEtSsx2DfCROmYD9USkmVeZqr2yOhEvo9NxY/zS/ZQfePgXHzN6YV3emfad33FMOULSuCwirYGzgDklJrUANgXcz+ToYmEO6zmAXBKOHBenTqfjxoSZ+7p/wZUdZ/DcuFymr7ITHcOZeL3ZJiJJwBTgGVX9qsS0NOCfqjrdvT8ReERV55WYrx9O0xEpKSmdhw4dWqUs2dnZJCUlVWlZL1U01+q9RWTM/Y4na35GvaK95CUks/akS9mR0snDbC1JSiqjScpHlqty/MqVUxjDU7NbsT+vBk+cX5vGtWJL5Kre/5Ohdjy5evToMV9Vu5Q6UVU9G4A4YDzwUBnTBwM3B9xfATQ71mN27txZqyo9Pb3Ky3qporn6fTRXUwcO1+zcRPXwbTtiSE9/IWTPZbkiM9fanc214xOf65WvfKSH8go0UHX/nwy148kFzNMy3iQvjxoS4F1gmaq+VMZso4DfukcPnQdkqepWrzJVZ+t2HWTC0u3cdl4atROsKchUH20abeHVm/7Nsm31eOwrO/M4HHm5j+BC4DbgUhFZ4A69RaS/iPR35xkLrAVWA28D93mYp1p7Z9pa4mKL+N0Fo/2OYkylXXrqPB667H+MXFCX92dM9DuOKcGzM4vVafc/5nGN7ubK/V5liBS7svMYPn8Tvzp7Eo3r2Ek6pnq6v8cwFm1uxzNju3Jas+Wc3/ZUvyMZl52SWg18NGsDeYXKXRfZ1oCpvmJilBdvfInWDbcw+pMhFL7YgW6Tr4WXOzpnzRvf2LWGwlxOfhEfz1rPZafNo12TtX7HMea41EnM4dPzBlB3glLjQL4zMmuTc+kUgNQb/QsXxWyLIMx9MX8Tew8VcG+3UX5HMSYoUr7PoabkHzmyIMe5hIrxhRWCMFZUrLwzbS1nnbiGLq1+8DuOMcFR1iVRyrqEivGcFYIwNn7JNjbuyeHeS0YidjkhEynKuiRKWZdQMZ6zQhCmVJXBU9fQuuEuLu8wxe84xgRPz1zn0igB8iUOeg7wKZCxQhCmvl+3h4Wbsrjr4pHExhT7HceY4EkthKtyILkYBbISavJw3j1MiLUtAr9YIQhTQ6aupUHtQ9zQeazfUYwJvtRC+HM2U7oPoOZfd7M6pRl/H7GB3dkH/E4WlawQhKHVOw4wcfkOfnv+aBLj8stfwJhqLL5GIS/9+iX259Tk8RHWf4EfrBCEobenriOhRiG/Pd9OIDPR4dSmG/jz5Z/wzZImfL1gst9xoo4VgjCzY38uI37M5IYu39Gg9j6/4xgTMv0uGUHnVksZ8PVOtmXt8TtOVLFCEGY+mLmeguJi7rbLSZgoExtTzIs3vExBUSx/+3KkNRGFkBWCMJKdV8gnszfQ6/Q5tG60we84xoRc60Zbeaz3+0xdmcKn30/wO07UsEIQRj6fu4n9uYX0u8QuJ2Gi163njuWidj/yzJhsNuy27klCwQpBmCgsKua96Wvp2noFZ52Y4XccY3wTE6M8f/2rxMYU8fAX4ygqtiYir1khCBNjFm1l875c7rGtAWNoXm8XA68azNz1Kbw73faXec0KQRhQVYZMXUvbxtvpeepUv+MYExZ+efYkLu8wixfGF7Nyu+0z85IVgjCwbE8xS7bs556LRxITY5vBxgCIwHO/fJ2kxEM8NGwSBUVFfkeKWBUqBCLSRESuE5H7ReROEekqIlZEgmTsugIaJWVz7Vnf+B3FmLDSKCmLZ697ncWbm/D6pBF+x4lYx/wyF5EeIjIeGANcCTQDOgD/BywSkSdFpK73MSPXsq37WbyriDsuHEViXIHfcYwJO706zuK6sybxeno8GZmr/I4TkcrrqrI3cI+qbiw5QURqAH2By4EvPcgWFd6etpaE2GJuOTfN7yjGhK2BVw1m1ppUHho2k7QH2pAYZ73sBtMxtwhU9a+lFQF3WqGqjlRVKwJVtDUrh1ELNnNJyyzq1drvdxxjwlZyrYP86/rXWL2jES9OsI7ug62i+wg+FpHkgPutRWSid7Giw/sz1qMU84tWdl0VY8rT7eQfuOXcsbwzvQ5z1i7yO05EqegO3+nAHBHpLSL3ABOAV461gIi8JyI7RGRxGdO7i0iWiCxwh6jqnmh/bgGfztlA706zaFzL9g0YUxF/7/0eJ9TfztLKh0kAABpTSURBVMPDF5Cdl+d3nIhRoUKgqoOBu4GvgUHAJapa3lkeHwC9yplnmqqe6Q6DKpIlUnw2ZyPZeUX0u9hOIDOmomon5PLCDa+Qubcez4793O84EaOiTUO3Ae8Bv8X5gh8rImccaxlVnQpYm0cp8guLeX/GOs4/aSmdWi7xO44x1UrXNku45+IRfDqnIZNXzPU7TkSoaNPQr4CLVPUzVX0M6I9TEI7X+SKyUETGicjpQXi8amH0wi1s259Hv262NWBMVTx0+SecnLKBR75cRdahQ37Hqfakqtf8FpF4VT1mP4oi0hpIU9WOpUyrCxSraraI9AZeVdX2ZTxOP6AfQEpKSuehQ4dWKXN2djZJSUlVWjZYVJV/zMgB8njqwrWIQHZ2S5KSMn3NVZZwzWa5KicSc63PSuCp2a05p2kB/c+oH+Rc/n9XlOZ4cvXo0WO+qnYpdaKqljngnDjW4BjTLwX6HmN6a2DxsZ4jYN71QKPy5uvcubNWVXp6epWXDZb05du11SNp+sW83nr4ZaWnv6AVWEW+DOGazXJZLlX05W9v1laPpOmYjGkaTOHwXVGa48kFzNMyVmR5Z2UsAkaLSC7wA7ATSATaA2cC3wHPVqU6iUhTYLuqqoh0xWmm2l2Vx6pOhkxdS0rd/Vx9hnW6Yczxur/HMCYu68rjI5pxTussGtdJLn8hc5Ty9hFcr6oXAuOBJUAssB/4BOiqqn9W1Z2lLSginwGzgFNEJFNE7hKR/iLS//BjA4tFZCHwGnCTW7Ui1uLNWcxcs5s7LhxFfI1Cv+MYU+3FxRbx0o0vcTA/nse++pII/wrxTHlbBJ1FpDlwC9CjxLSaQE5ZC6rqzcd6YFV9HXi9IiEjxeCpa0lKyOc359r11Y0JlvYpm/jbFR/x9Ji7GT5/Ejd06el3pGqnvC2Ct4CJwKnAvIBhvvvXVNCmPYcYu2gLN3f9hrqJB/2OY0xEuePCUXRtvZhBo/ewed8uv+NUO+Vda+g1VT0NeE9VTwoY2qjqSSHKGBHem7EOoZg7LrRDRo0JttiYYl644WWKVPjrF6Motu4tK6WiZxb/3usgkSzrUAGfz93I1WdMo3m9bX7HMSYindhwO//X5x1mrknh49nj/I5TrVjnMiHwyZwNHMov5u6Lbd+AMV66uet4up08j+fG5bJ25xa/41QbVgg8lltQxPsz1nFx+ww6NF/udxxjIpoI/OtX/yE+toC/fDGewqJivyNVC1YIPPb1gs3sys7n3kts34AxodA0eTdPXftfTshcyaHn28HAevByR8iwfgzKYt38eKi4WBkydS0dmm3iwnaz/Y5jTNS4OmYGvRIWkZDnnq+TtQlGP+jcTr3Rv2BhyrYIPDRp+Q7W7DzIvd1GIuJ3GmOih0xMJEFLnLRZkAMTo+pq9xVmhcBDQ6aupXnyPnp3+s7vKMZEl6wyfnllhd+F98KBFQKP/LhxL9+v38OdF31NXGyR33GMiS7JZZxHkNwytDmqCSsEHhkydS11EvO4qesYv6MYE3165kLckcUgT+KgZ1T1iFthVgg8sGH3Qb5Zso1bzxtDUoJ1mmFMyKUWwlU5kFwMKAcSEvlr3j2Mj23qd7KwZEcNeeCdaeuoEVPMHRfYCWTG+Ca1EFKzAUgsOsTK/7Rg7qiNXNgul6SERJ/DhRfbIgimjGEUvXQ6T/54Ed/X6k+T9Xv9TmSMwblc9TPXvcG2/cm8NME6vS/JCkGwZAyD0Q8Suz+TGFHqF2TD6JqQYRtdxoSDzq2W85uu3/DBzAYs3mxn+QeyQhAsEwc5xykHKhCYaJugxoSLv/X6kAa1s/j7iBkUFdvlJw6zQhAsZR2fXNbxzMaYkEuueZABV71NRmZTPp5ll305zApBsJR1fHJZxzMbY3xxVepULm7/Ay9MKGRbVqk97UYdKwRBUtjjH+QQf+TIOHWOZzbGhA0RePraNykoiuHJ0SP9jhMWrBAEybTEHjySfzc5teIAdY5fvirHOYTNGBNWWjXcxoM9hzJucXMmLpvhdxzfWSEIktEZW0iP70LsQ1kw8AD8OduKgDFh7J6LR9C+yQYGfL2WQ/nRveVuhSAI8gqL+HbJNq44fSbxNezL35jqIL5GIc/+8g0272vAq9994XccX1khCIJpK3dxIK+Ivqlz/I5ijKmEc1ov5aZzxvPO9GSWblnldxzfeFYIROQ9EdkhIovLmC4i8pqIrBaRDBE526ssXkvL2EJyzRzrfMaYaujRK9+nXs0D/H3EVIqLo/MoPy+3CD4Aeh1j+pVAe3foB/zXwyyeyS0o4tul2+h1+gy73LQx1VC9Wtn8X993WLCpKf/7PjqvD+ZZIVDVqcCeY8xyDfCROmYD9USkmVd5vDJl5U4O5hfT9wzbGjCmurr2zMlc2G4Bz3+Tx479u/2OE3J+7iNoAWwKuJ/pjqtW0jK2Ur/WIc4/6Xu/oxhjqkgEnrrmTfIK4hiUNsLvOCEnqt61iYlIayBNVTuWMi0N+KeqTnfvTwQeUdV5pczbD6f5iJSUlM5Dhw6tUp7s7GySkpKqtGxp8oqUBycd4vxm+7i947YqP052dkuSksKzC71wzWa5KsdyVczXqxsyYnVj7ju9iK4n1PU7zlGO5zusR48e81W1S6kTVdWzAWgNLC5j2mDg5oD7K4Bm5T1m586dtarS09OrvGxpxmZs0VaPpOmMVV31eFZVevoLx7W8l0O4ZrNclsuLIbeghvZ44b/aZeAIPZSXp+HmeL7DgHlaxgv3s2loFPBb9+ih84AsVd3qY55KS8vYSqOkbLq2OWojxhhTDSXUKOSZa99kZ04c/5k0zO84IePl4aOfAbOAU0QkU0TuEpH+ItLfnWUssBZYDbwN3OdVFi8cyi9k4vLt9Oo4nRqxdjlbYyLF+W0XcWHzLIZMrcPK7Wv8jhMSnvWaoqo3lzNdgfu9en6vTVq+g9yCYvqmzvI7ijEmyG46dQdL96Xw96/SGXbvScTERPbl5O3M4ipKW7iVxnUOcE7rH/2OYowJsjrxRTzW+z3mbWjGsHlj/Y7jOSsEVZCdV0j6iu307jiN2BhrFjImEt3Q+Tu6tlnEc+Oy2ZW9z+84nrJCUAUTl20nr1Dpe4Y1CxkTqUTg2eve4FB+Is+MGe53HE9ZIaiCtIytpNTdT+cTF/gdxRjjoXZNMunfbTgjfmzG9FVz/Y7jGSsElXQgt4ApK3bQu9NUYmKi8wJVxkST+3sMo3XDLfzfyKXkFhT4HccTVggq6btl28kvUjtayJgokRiXz9PXvsH63Y14Mz0y+y2wQlBJaQu30jx5H2edkOF3FGNMiFzUfiHXnpnOf6fUZvWO9X7HCTorBJWQlVPA1FU7rVnImCj0eJ93qRmXy+MjvsM5DSpyWCGohG+XbqegyI4WMiYaNa6zj8d6v8+cdc0YPn+833GCygpBJaRlbKFFvT2c0XKR31GMMT74dZcJdGm1hGfH7mPPwSy/4wSNFYIK2ncon+mrdtI3dSoS2WebG2PKEBOjPHPdmxzIrcmzYyPn3AIrBBU0Ycl2Couhb+pMv6MYY3x0StMN3HPJCIbPb8qsNT/4HScorBBU0OiMLZzYYBcdWyz1O4oxxmcPXjqUExps4/GRGeQVVv9zC6wQVMCeg/nMXLOLPtYsZIwBasbnMeia/9Jx9wry/n0yDKwHL3eEjOrZh4Fnl6GOJOOXbKOoGPqmzvA7ijEmTPTIW8gFCetIyCt0RmRtgtEPOrdTb/QvWBXYFkEFpGVsoU2jHXRotsLvKMaYcDExkQQtPHJcQQ5MHORPnuNghaAcu7LzmLVmN306TbNmIWPMz7LK+ELIygxtjiCwQlCObxZvo1ih7xnT/Y5ijAknyWWcXZzcMrQ5gsAKQTnSMrbQtvE2TklZ5XcUY0w46ZkLcUcWg/yYOOg5wKdAVWeF4Bh2HMhlzro99Em1ZiFjTAmphXBVDiQXA8reuNo8kn8Xq5t28TtZpdlRQ8fwzeJtqELfVGsWMsaUIrUQUrMBKMqOYeILZ7Nz1Hd8fNc9SDX69WhbBMeQtnArJ6ds4eSUNX5HMcaEuUZJWfzlF58wfXULxi2e5HecSrFCUIZtWbnM3bCHPp2m+R3FGFNN3HLuWE5rtpan07ZwKD/X7zgV5mkhEJFeIrJCRFaLyKOlTL9dRHaKyAJ3uNvLPJUxbvFWVKFPqhUCY0zF1Igt5qlr/suWrAa8kV59zjL2rBCISCzwBnAl0AG4WUQ6lDLr56p6pju841WeykrL2MqpTTNp12S931GMMdVIl9bL+OVZk3h7al3W7drgd5wK8XKLoCuwWlXXqmo+MBS4xsPnC5ot+3KYv2EvfW1rwBhTBY/2fo+EGvkMHDW+WvRm5mUhaAFsCrif6Y4r6VcikiEiw0XkBA/zVNjYRVsBaxYyxlRNkzr7+NPl/2PKyhZMWDrF7zjlEq+qlYhcD/RS1bvd+7cB56rqHwLmaQhkq2qeiNwL/FpVLy3lsfoB/QBSUlI6Dx06tEqZsrOzSUpKKne+QbNyKNIcnrxgXZWep7Kys1uSlBSep6WHazbLVTmWq3KCkauoGJ6Y2ZqcwlieuziZ+NjjP5y0ot9hpenRo8d8VS39JAdV9WQAzgfGB9x/DHjsGPPHAlnlPW7nzp21qtLT08udZ+Pug9rqkTR9I/03Xq2ao4b09BdC9lyRks1yWa7qkGvWmo7a6pE0fXHCxxoMFfkOKwswr9SQqp42Dc0F2otIGxGJB24CRgXOICLNAu5eDSzzME+FjFvsNAv17RT+m3PGmPB23kmLufqMybw1pTYbdm8qfwGfeFYIVLUQ+AMwHucLfpiqLhGRQSJytTvbgyKyREQWAg8Ct3uVp6LSMraS2nIdJzbc7HcUY0wEeLzPe8TFFDFo9Di/o5TJ0/MIVHWsqp6sqm1V9Rl33ABVHeXefkxVT1fVM1S1h6ou9zJPeTbuPkRGZhZ9OlkHNMaY4Eipu4c/XvYpE5e3YOKy8DwAxc4sDjDmp6OFJvsbxBgTUW6/YDRtG2/iydFryS3I9zvOUawQBEjL2MKZJ6yhZf1tfkcxxkSQ+BqFDLrmLTbuacSQqcP9jnMUKwSudbsOsmTLfuuX2BjjiQvbLaRPp2m8kV6TTXvCax+kFQLX4ZPIetvRQsYYjzze511ipJinx6T5HeUIVghcoxduoXOrVTSvt93vKMaYCNW83i7+cOnnjF/SkikrZ/od5ydWCIDVO7JZvu0AfTqFzxtjjIlMd188gjaNNjNw1EryCgv8jgNYIQCcZiERpXenyX5HMcZEuIQahQy8ejDrdjXmnWnhsePYCgHO0ULntFpB0+SdfkcxxkSBbif/wBWnz+T1SfFs2ef/UYpRXwhWbj/Ayu3Z9Emd5XcUY0wU+UfftylW4Zkxo8qf2WNRXwjGZDjNQld2Svc7ijEmirSsv5P7e3zBmEUtmL5qtq9ZoroQqCppGVs4t80ymtTZ43ccY0yU6XfJl7RquIUnRi0jv7DItxxRXQhWbD/Amp0HrVnIGOOLxLgCnrhqCGt2NuGDmf7tOI7qQjAmYysxolzZ0ZqFjDH+uPTUeVx22hxe/S6W7ft3+JIhagvB4Wah89suoVHSPr/jGGOi2IC+QygojuWZMSN9ef6oLQRLt+5n3a5D9OlkzULGGH+d2HA7/bsNZ9TCFsxaMzfkzx+1hWBMxlZiY4rp1XGy31GMMYb7ug+nZf3tDBy1iIKi0O44jspCcLhZ6IK2i2hQO8vvOMYYQ2JcPgP6DmHF9hQ+mjUipM8dlYVg8eb9bNyTQ99Uf4/dNcaYQJd3mEO3k+fxyrfKjgO7Q/a8UVkI0hZtoUZMMVecPtnvKMYY8xMRGHj1EPIK4/jn2C9D9rxRVwhUlTEZW7io/ULq1TrgdxxjjDlCm0ZbuOeSr/jqxxbMXf9DSJ4z6grBwswsMvfm0qfTHL+jGGNMqe7vMYzmyTsZ8PWPFIZgx3HUFYIxGVuIiy3iF6fbSWTGmPBUKz6P/+v7Dsu2NuV/c772/PmiqhAUqzImYyuXtF9Acs2DfscxxpgyXdlxBhe1+5EXJhSyK9vba6F5WghEpJeIrBCR1SLyaCnTE0Tkc3f6HBFp7WWetfuK2ZKVS59UaxYyxoQ3Z8fxYHILEnj+G293HNfw6oFFJBZ4A7gcyATmisgoVV0aMNtdwF5VbSciNwH/An4d9DAZw2DiIO7KyuTKhAY0UOuX2BgT/to1yeTOi0aydVpT8tadTLeDO+DHltBzAKTeGLTn8awQAF2B1aq6FkBEhgLXAIGF4BpgoHt7OPC6iIiqatBSZAyD0Q9CQQ4CtJDd8E0sxNWA1MKgPY0xxnjhzynD0PiaJBx0+zfO2uR8p0HQioGXTUMtgE0B9zPdcaXOo6qFQBbQMKgpJg6CgpwjxxUITEwM6tMYY4wXEqfEUJMSndwX5DjfbUHi5RZB0IhIP6AfQEpKCpMnT67wst2yMpFSxmtWDFMmvxScgMcpO7sFk8MkS0nhms1yVY7lqpxwytUta2AZ32GZTKnEd+GxeFkINgMnBNxv6Y4rbZ5MEakBJANHnVetqkOAIQBdunTR7t27VzzFjy2dTakSJPkEunf/c8Ufx0OTJ0+me/fgtfcFU7hms1yVY7kqJ6xy/fhuGd9hLanUd+ExeNk0NBdoLyJtRCQeuAko2UvzKOB37u3rgUlB3T8Azk6VuJpHjour6Yw3xphwF4LvMM+2CFS1UET+AIwHYoH3VHWJiAwC5qnqKOBd4GMRWQ3swSkWwXV4Z8rEQWhWJpIc/D3uxhjjmRB8h3m6j0BVxwJjS4wbEHA7F7jBywyAs8JSb2TK5MlB25QyxpiQ8fg7LKrOLDbGGHM0KwTGGBPlrBAYY0yUs0JgjDFRzgqBMcZEOQn2YfteE5GdwIYqLt4I2BXEOMESrrkgfLNZrsqxXJUTiblaqWrj0iZUu0JwPERknqp28TtHSeGaC8I3m+WqHMtVOdGWy5qGjDEmylkhMMaYKBdthWCI3wHKEK65IHyzWa7KsVyVE1W5omofgTHGmKNF2xaBMcaYEiKmEIhILxFZISKrReTRUqYniMjn7vQ5ItI6YNpj7vgVInJFiHM9JCJLRSRDRCaKSKuAaUUissAdSl7C2+tct4vIzoDnvztg2u9EZJU7/K7ksh7nejkg00oR2Rcwzcv19Z6I7BCRxWVMFxF5zc2dISJnB0zzcn2Vl+sWN88iEZkpImcETFvvjl8gIvNCnKu7iGQFvF8DAqYd8zPgca6/BmRa7H6mGrjTPFlfInKCiKS73wNLROSPpczj7edLVav9gHOZ6zXASUA8sBDoUGKe+4C33Ns3AZ+7tzu48ycAbdzHiQ1hrh5ALff27w/ncu9n+7i+bgdeL2XZBsBa929993b9UOUqMf8DOJc393R9uY99CXA2sLiM6b2BcYAA5wFzvF5fFcx1weHnA648nMu9vx5o5NP66g6kHe9nINi5Ssx7FU4fKZ6uL6AZcLZ7uw6wspT/R08/X5GyRdAVWK2qa1U1HxgKXFNinmuAD93bw4GeIiLu+KGqmqeq64DV7uOFJJeqpqvqIffubJye3LxWkfVVliuAb1V1j6ruBb4FevmU62bgsyA99zGp6lScPjPKcg3wkTpmA/VEpBnerq9yc6nqTPd5IXSfr4qsr7Icz2cz2LlC8vlS1a2q+oN7+wCwjKP7d/f08xUphaAFENiXWyZHr8if5lHVQiALaFjBZb3MFegunKp/WKKIzBOR2SJybZAyVSbXr9zN0OEicrjb0bBYX24TWhtgUsBor9ZXRZSV3cv1VVklP18KTBCR+eL0Cx5q54vIQhEZJyKnu+PCYn2JSC2cL9QvA0Z7vr7EabI+C5hTYpKnn69q0Xl9NBCRW4EuQLeA0a1UdbOInARMEpFFqromRJFGA5+pap6I3IuzNXVpiJ67Im4ChqtqUcA4P9dXWBORHjiF4KKA0Re566sJ8K2ILHd/MYfCDzjvV7aI9AZGAu1D9NwVcRUwQ1UDtx48XV8ikoRTeP6kqvuD9bgVESlbBJuBEwLut3THlTqPiNQAkoHdFVzWy1yIyGXA48DVqpp3eLyqbnb/rgUm4/xSCEkuVd0dkOUdoHNFl/UyV4CbKLHZ7uH6qoiysnu5vipERFJx3sNrVHX34fEB62sHMILgNYmWS1X3q2q2e3ssECcijQiD9eU61ucr6OtLROJwisD/VPWrUmbx9vMV7B0ffgw4WzZrcZoKDu9gOr3EPPdz5M7iYe7t0zlyZ/FagrezuCK5zsLZOda+xPj6QIJ7uxGwiiDtNKtgrmYBt68DZuvPO6fWufnqu7cbhCqXO9+pODvuJBTrK+A5WlP2zs8+HLkz73uv11cFc52Is9/rghLjawN1Am7PBHqFMFfTw+8fzhfqRnfdVegz4FUud3oyzn6E2qFYX+7r/gh45RjzePr5CtrK9XvA2au+EudL9XF33CCcX9kAicAX7j/F98BJAcs+7i63ArgyxLm+A7YDC9xhlDv+AmCR+4+wCLgrxLmeA5a4z58OnBqw7J3uelwN3BHKXO79gcA/Syzn9fr6DNgKFOC0w94F9Af6u9MFeMPNvQjoEqL1VV6ud4C9AZ+vee74k9x1tdB9nx8Pca4/BHy+ZhNQqEr7DIQqlzvP7TgHkAQu59n6wmmuUyAj4H3qHcrPl51ZbIwxUS5S9hEYY4ypIisExhgT5awQGGNMlLNCYIwxUc4KgTHGRDkrBMYYE+WsEBhjTJSzQmDMcRKRc9yL8yWKSG33mvId/c5lTEXZCWXGBIGIPI1z9npNIFNVn/M5kjEVZoXAmCAQkXhgLpCLc7mEonIWMSZsWNOQMcHREEjC6WEq0ecsxlSKbREYEwRuH8lDca6a2UxV/+BzJGMqzDqmMeY4ichvgQJV/VREYoGZInKpqk4qb1ljwoFtERhjTJSzfQTGGBPlrBAYY0yUs0JgjDFRzgqBMcZEOSsExhgT5awQGGNMlLNCYIwxUc4KgTHGRLn/Bxp+DvQCJLw2AAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(np.linspace(0, 12, 12 + 1) * 0.166667 + 0, f(np.linspace(0, 12, 12 + 1) * 0.166667 + 0))\n",
        "plt.plot(np.linspace(0, 12, 12 + 1) * 0.166667 + 0, f(np.linspace(0, 12, 12 + 1) * 0.166667 + 0), 'o')\n",
        "\n",
        "plt.fill_between(np.linspace(0, 12, 12 + 1) * 0.166667 + 0, f(np.linspace(0, 12, 12 + 1) * 0.166667 + 0), color='yellow')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('f(x)')\n",
        "plt.title('Integral 1 - Área: Simpson 3/8')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nakSxVwJ0s5r"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 5. Integración - Integral 1 - Área: Simpson 3/8\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "cGZnD7kxPu2W",
        "outputId": "02b6421e-4a4e-4289-8d83-8378c2bbf075"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(list(map(lambda x: x[0], np.array(table1, dtype=np.int8))), list(map(lambda x: x[1], np.array(table1, dtype=np.float64))), label='Intervalo')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table1, dtype=np.int8))), list(map(lambda x: x[2], np.array(table1, dtype=np.float64))), label='Resultado')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table1, dtype=np.int8))), list(map(lambda x: x[3], np.array(table1, dtype=np.float64))), label='Error')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table1, dtype=np.int8))), list(map(lambda x: x[1], np.array(table1, dtype=np.float64))), 'o')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table1, dtype=np.int8))), list(map(lambda x: x[2], np.array(table1, dtype=np.float64))), 'o')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table1, dtype=np.int8))), list(map(lambda x: x[3], np.array(table1, dtype=np.float64))), 'o')\n",
        "\n",
        "plt.xlabel('n')\n",
        "plt.title('Integral 1: Simpson 3/8')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mmP-Hh_o05jT"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 6. Integración - Resultados primer integral\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wmF2AHuq1GEt"
      },
      "source": [
        "Segunda integral"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "3_Uv6uHFOrzH",
        "outputId": "53347902-58ba-4574-90e7-2a052ff45317"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-2748deb1-aa0e-4063-9a3a-b05e6987f28c\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>Intervalo</th>\n",
              "      <th>Resultado</th>\n",
              "      <th>Error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>3.0</td>\n",
              "      <td>0.666667</td>\n",
              "      <td>-4.0</td>\n",
              "      <td>3.792593</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>6.0</td>\n",
              "      <td>0.333333</td>\n",
              "      <td>-4.0</td>\n",
              "      <td>0.118519</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>9.0</td>\n",
              "      <td>0.222222</td>\n",
              "      <td>-4.0</td>\n",
              "      <td>0.015607</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>12.0</td>\n",
              "      <td>0.166667</td>\n",
              "      <td>-4.0</td>\n",
              "      <td>0.003704</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>15.0</td>\n",
              "      <td>0.133333</td>\n",
              "      <td>-4.0</td>\n",
              "      <td>0.001214</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2748deb1-aa0e-4063-9a3a-b05e6987f28c')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-2748deb1-aa0e-4063-9a3a-b05e6987f28c button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-2748deb1-aa0e-4063-9a3a-b05e6987f28c');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "      n  Intervalo  Resultado     Error\n",
              "0   3.0   0.666667       -4.0  3.792593\n",
              "1   6.0   0.333333       -4.0  0.118519\n",
              "2   9.0   0.222222       -4.0  0.015607\n",
              "3  12.0   0.166667       -4.0  0.003704\n",
              "4  15.0   0.133333       -4.0  0.001214"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table2), columns=['n', 'Intervalo', 'Resultado', 'Error'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RE_X48sl1Ja-"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 3. Integración - Resultados segunda integral\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "KmiwylPddBwo",
        "outputId": "72f05863-5143-41d2-8314-bf88a8b2034e"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "WARNING:matplotlib.legend:No handles with labels found to put in legend.\n"
          ]
        },
        {
          "data": {
            "image/png": 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Ud43qyy/bGvHCFyd5HccYE8Hm/9yZ7bkpjOz8O1AvpMu2QnGYBrZLZXinBP71yen8trOB13GMMRFqxtL+JMbmMbh9RsiXbYWiEtx+Qj9UY3jgw0u8jmKMiUBFxVF8tKw/Q478lsS40O52AisUlSKtTg2uHNKCD5f053+ru3odxxgTYRb+0oEtu+syovN6oGHIl2+FopKMH9iJI+oWcufUyykoivY6jjEmgkxfkkF8TD5DjuzjyfKtUFSShNhoJp7Qm9Wb03jpy9BdCGOMiWzFxcJHS/szqN13JMV7c9KMJ4VCROqKyGwR+dH9W8fPdEUissi9TQ11zvLK7NCIIe1jeezjM9m8q9SXZIwx5fLduvZs3FWfEV1+ARp7ksGrLYqbgTmq2haY4z4uzV5V7ebeTgxdvIoRESaOyiC/MJ5JMy7yOo4xJgLMWJJBbHQhmR16eJYhxqPljgYGu/dfAuYCN3mUpVK1rF+TSwY2Zd2nMez7tQ7xuYWQopCZB+mFXsczxlQhqs5psUe3XUSthAs9yyHqQQ88IrJTVWu79wXYsf9xiekKgUVAITBJVd8r4znHA+MBUlNTe0yePLlC2XJyckhKOrweo+psmEu7VU+SSP4fw4qiYlnZ/gQ2p3apYK40kpLWH1auYLBc5WO5yqe65/o5O4G7v2rBRZ23cnRa8wByVfz7a8iQIQtVtfT2iFQ1KDfgY2BpKbfRwM4S0+7w8xxN3b+tgLVA60CW3aNHD62orKysCs/7h0c6qd5Z6+DbI0mHiu73lpX1cIXnDebNclkuyxW824PTz9PWt7ynO3L/oYE4nO8vYIG/IEHb9aSqw/yNE5FNItJYVX8XkcbAZj/P8Zv7d42IzAW6Az8FI2+lyvbzSyNbQpvDGFNlqTqNAPZvs4TaNc72NItXB7OnAue5988D3i85gYjUEZF49359IAP4IWQJD0dKmp/h1tG2MSYwP/zekl+2NWFk51VAC0+zeFUoJgHHiMiPwDD3MSLSU0Sed6fpACwQke+BLJxjFFWjUGROhNjEAwYVRYtzQNsYYwIwY0kG0VFFHNups9dRvDnrSVW3AZmlDF8AXOze/xKo2JFfr6WPdf7OuQfNXs8m6vJi7DBu6PQi1hi5MeZQVGH6kgH0afkDdWt63+WyV6fHRr70sZA+FgGW/vA7z778LfW+2Malg/7rdTJjTJhbtak5a7amccGAL4E2XsexJjxCYVjHxgzrEMdjH5/Jhp31vY5jjAlz05dkIFLMcZ3aeR0FsEIRMneOykCJ4Z5p1se2MaZsM5Zm0KvFChomn+J1FMAKRcg0q1uDCZmt+GhZX7Ksj21jjB+rN6exalNzRnZeChzpdRzACkVIXTygE60bFDJx6uXkFcR5HccYE4Y+WtofgOGdW3uc5E9WKEIoLiaKe8dksG57Kk9ljfU6jjEmDE1fkkGP5itolHKy11H+YIUixPq3rs+YbjV5+tNTWLOliddxjDFhZO3Wxvzwe2tGdF4MdPI6zh+sUHjg1uP7Eh8LE9+/CrWLtY0xrhl/7HZqDoRPkz9WKDzQMDmBG47rwBer0/lg8dFexzHGhIkZSzPomraatDre9GTnjxUKj5zVpx2dmxZz7weXsDsv8dAzGGMi2rrtDVm8vh0junwHdPM6zgGsUHgkOkq4b8wAtuTU4dHZ53gdxxjjsY+WZgAwonNTwmm3E1ih8FS3ZnU4s3cd/u/LE1i2oaXXcYwxHpq+NINOTX6meb0xXkc5iBUKj914XG/q1Cji9veuprg4vH5FGGNC4/fsenz365GM7LIACL8Lcq1QeCylRiy3juzKd7+2Y8qCY7yOY4zxwP6L7EZ0TiXcdjuBFYqwcPJRLejdQpj00QVsz63ldRxjTIjNWJLBkY1+pVWD8NvtBFYowoKIcO+Yo8nJq8GkGRd6HccYE0Kbd9Xhm186MrzzAqCP13FKZYUiTLRvlMxFAxozZcEwFqzt4HUcY0yIzFzWD9UoRnapQ7h+JYdnqmpqQmZ3mqQUcPt7V1FYZG+NMdXB9CUZtG7wG20bjvI6il/2bRRGasbHMHFUL1ZsbM7/fRm+HxpjTOXYmpPC1z93ZmSX+YgM8DqOX1YowsxxnZowpH0Mj84+m43Z9byOY4wJolnL+lKs0YzonAxEex3HLysUYUZEuPvEoyksjuXeDy71Oo4xJohmLM2gRb2NdGh8gtdRymSFIgwdUa8GVw5pwYdL+vPpqqO8jmOMqWyLYyh6JJmXfn2Y9wtuR5Zs8TpRmaxQhKlLB3WmZf1C7nz/cvIKYr2OY4ypLItjYFoi0buEKIGU/D0w7VpYPMXrZH55UihE5DQRWSYixSLi93p1ERkuIitFZLWI3BzKjF6Lj4nmntH9WLutMc98eqrXcYwxlWVOAhSUuPq6YC/MucebPAHwaotiKXAy8Jm/CUQkGngSGAF0BM4QkY6hiRcejm7bkBPSE3ly7mlsyrWtCmMiQrafJjqy14c2Rzl4UihUdbmqrjzEZL2B1aq6RlXzgcnA6OCnCy93nNCfuGjhleWNrDc8YyJBip9/5JS00OYoh3A+RtEUWOfzeL07rFpJrZXAdce0Z+nWmn80HGaMqboKh+SzlxJ7CGITIXOiN4ECIBqkn6ki8jHQqJRRt6nq++40c4HrVXVBKfOfCgxX1Yvdx+cAfVT1Kj/LGw+MB0hNTe0xefLkCuXOyckhKSmpQvMGS1Gx8vnnsxhf/CaNZRv74lNY02oom1O7eB2NnJw0kpLCb5PZcpWP5Sqfw8n1zcZk1i3+mftqvEFy4U72xddnTatz2Jw6qBJyVfz7a8iQIQtVtfRjxqrq2Q2YC/T0M64fMNPn8S3ALYE8b48ePbSisrKyKjxv0Hz/pubf1UD1zlp/3u5LVv0+Rj18+1QVzcp62PMMlstyVaVcZzx7v/Z/8D9aWPS2VrbD+f4CFqif0OG86+kboK2ItBSROGAcMNXjTN6Ycw+xuu/AYQXinD1hjKkyVm9O48ufunJmn0+IjjrR6zgB8+r02JNEZD3OVsOHIjLTHd5ERKYDqGohcBUwE1gOTFHVZV7k9Zy/syH8nT1hjAlLr309gtjoAk7v1RpKHqcIYzFeLFRV3wXeLWX4BmCkz+PpwPQQRgtPKWmQva6U4XYalDFVxZ78eN5emMmIzvOon3S113HKJZx3PZn9MidSFBV/wKC9GseW3rbryZiqYuqiQezOS+KcfpuoaidwWqGoCtLHsrL9lZDSDBAKk9O4iwu4etn1qG1UGBP2VOGVeSM5stEv9Gx+ttdxys0KRRWxOXUQXLcU7tpJzF+X0XXkxcxb05nJ3xzndTRjzCEsWteOZRvacFbfLxAZ6nWccrNCUUWN69WWvq2EBz68yPqtMCbMvTLveGrG7eWk7n2AqncSihWKKioqSph08iDyi+K44/0rbBeUMWFqe24tPlh8NCcf9SlJ8ed5HadCrFBUYS3q1+S6Y1ox+4c+TF+S4XUcY0wp3lowjPzCOM7uWwzU9jpOhVihqOIuHtCJzk2LuHPq5ezcE15NjxhT3RUXC699PYLeLX6gfaOLvI5TYVYoqriY6Cj+dsogduypxX0fXuJ1HGOMj89+7M6v2xtzdr/vgKrbW6UVigjQqUkKlw5sxNsLM/lsVXev4xhjXK/OO576STsZ3mm411EOixWKCDEh8yha1S/g1nevJnefXYhnjNfW72jAnBW9GNfrE+Jixnod57BYoYgQCbHRTDplAOt3NOQfs87xOo4x1d4b84cjKGf0aQBU7R9vVigiSO+W9Tm7bwr/+XIU3/7a3us4xlRb+wpjePObYxl65Lc0rV31jx1aoYgwNw3vQ6Nahdz8zrXkF3rS5qMx1d5HS/uzNacO5/T7CWjtdZzDZoUiwiQnxHL/SX1ZtakZT809zes4xlRLr847nub1NnJ0m6p9bGI/KxQRaOiRjTmxayJPZp3Oqk1HeB3HmGplxcbmfLO2E2f1mUtU1MhDz1AFWKGIUHeOyiApvpgb376WomJ7m40JlVfnjSQuJp/TenQEor2OUynsGyRC1UuK585R3Vm0rh0vfXmC13GMqRZ25yXy7rdDGJX+P+rUrLpXYpdkhSKCje7WnMHto3lo5rms257qdRxjIt573w0hN78G5/TbCTT0Ok6lsUIRwUSE+08aRJREc+u7E6yFWWOCSNXZ7dSl6U90TauarcT6Y4UiwjWtnchNI47k8x+78s63Va/DFGOqim/WdmLlphac3XceIgO8jlOprFBUA2f3aU/P5sq9H4xny+6q2cyxMeHulXkjSU7I5cSuR1MVOycqixWKaiAqSph0ymD25idy19TLvY5jTMTZsrs2Hy3tz2k9skiMq3p9Yh+KFYpqok3DJCZkHsGHSzKYuayv13GMiShTFhxDQVEsZ/WNA5K9jlPpAioUItJQRE4SkStF5EIR6S0iFS4yInKaiCwTkWIR6VnGdGtFZImILBKRBRVdnnFcOiidIxsVcsd7V5C9t6bXcYyJCEXFUbw2bwQZbRbTukHVb9epNGV+2YvIEBGZCXwIjAAaAx2B24ElInK3iNSqwHKXAicDnwUw7RBV7aaqfguKCUxsdBR/P3UgW3NqM2lG5JzjbYyXPlnRkw3ZDTmn71Kgs9dxguJQrcaNBC5R1V9LjhCRGOAE4BjgnfIsVFWXu89RntlMJUhPq8PFRzfk2c+OZVTXLPq3XuJ1JGOqtFfmHU9qre0M6zDK6yhBU2ahUNUbyhhXCLxX6YlKLAaYJSIKPKOqzwZ5edXCdcN6MnPZVD5+cwB9E9YStQtIUcjMg/RCr+MZU2X8sq0Rn63qwXXD3iImOnK/nkQDuApLRF4BrlLVbPdxC+AFVc0sY56PgUaljLpNVd93p5kLXK+qpR5/EJGmqvqbiDQEZgNXq2qpu6tEZDwwHiA1NbXH5MmTD/m6SpOTk0NSUlKF5g2mys5VsDqLjHVPUUPy/xhWFBXLyvYnsDm1SzlypZGUtL7SclUWy1U+lqt89ueavKIBs36pyz8G7aJOQhOvYx3W98SQIUMW+t3Fr6qHvAGXAitwd0UBq4BRgcx7iOedC/QMcNq7cIrKIaft0aOHVlRWVlaF5w2mSs/1SCfVO2sdfHskScvzNmZlPVyu6UN1s1yWK9i59ubHade7X9fLX71NVX/RcHA43xPAAvXzggPq2UZVnxGRZUAWsBXorqobK1S2AiQiNYEoVd3t3j8WuCeYy6xWsv38Ssu240bGBOKDxQPYuacWZ/ddD0R2c/6Bnh57DvAicC7wf8B0Eela0YW6p9quB/oBH7pnViEiTURkujtZKvCFiHwPzAc+VNWPKrpMU0JKmp/h1iCUMYF4dd5IWjf4jX6txnkdJegC7SvzFGCAqm4G3hCRd3EKRveKLFRV3wXeLWX4BpzdW6jqGqDCxcgcQuZEmDYBCvb+MagoWojOzPMwlDFVw9rseBata8mdo95A5GWv4wRdQFsUqjrGLRL7H88H+gQtlQm+9LEw6nFIaYYibIqqx8Ti89ncMvwO5BsTbj5ZV4fE2DxOPqo71aGBi0NdcHe7iNQtbZyq5ovIUBGxXnGqqvSxcN1S5K6d7Lp0EW8XDOGGt/6C2t4nY/zK3lOTeRtqMab756Qknu91nJA41K6nJcA0EckDvgW2AAlAW6Ab8DHwQFATmpBom1qLW0e24c6pMbz81Qmc1/8DryMZE5be+TaT/OIozu6bB9TzOk5IHGqb6VRVzQBmAstwOoDdBbwK9FbV61R1S5AzmhA5t19HBrcXHph+IT9uauZ1HGPCjrqdE7VO2UunJhd6HSdkDlUoeohIE+AsYCrwDPAy8A2QGORsJsREhL+fOpSa8cqEyTexrzDQcx2MqR6+/Kkra7amMfSIHKCX13FC5lCF4mlgDnAksMDnttD9ayJMw+QE/n5KL5b/3oJ/zDrX6zjGhJVXvhpJnRq76NUoiUjrnKgsZRYKVX1cVTsAL6pqK59bS1VtFaKMJsSGdWzGWX2SeO7zMXy5Ot3rOMZ4b3EMhf+oxVOrn2RuzF9I21q9GtMM9PRY6xatmrn9+AG0rF/IX6b8lZ177JRZU40tjoFpicTshiiBlPw9tF/5b1g8xetkIRP5JwCbCkmMi+afp6gs5o0AABwdSURBVA9ha05tbn13gp0ya6qvOQlQcOBupujifTCn+rQoZIXC+NUlrTZ/ObYZ05f05+2FfhsKNiay+Wv/zF97aRHICoUp06UDu9G7pXLX1Mv4ZVtprcYbE9mK/fXh6a+9tAhkhcKUKTpKePT0TKKiornuzRsoLLKPjKleZjXuxh6NO2BYUVS8015aNWH/9eaQmtZO5P6TuvLtr+15Iut0r+MYEzJbc1L46/KreSN1CKSkAgIpzVjZ/kqnCZxqwq6oMgE5sWsrslas4V+fjGNgu2856oiVXkcyJugen3MGeYXxDDmtNjRY9cfwzXPn0tHDXKFmWxQmYHePHkSjWoVcO/kGcvbZhfkmsq3Z0oTXvx7Omb1n06pB9dnNVBorFCZgtRJieWzcQNbvaMhdUy/zOo4xQfXQzPOIjylgQmZNoPocuC6NFQpTLr1a1OeKwam8vTCT6UsyvI5jTFB8+2t7ZizNYPzAaTRIvtnrOJ6zQmHK7ZphPemaVsgt/72a7Xl2mMtEFlV4cPqF1E/aycVHdwVqex3Jc1YoTLnFRkfx2LhhFBTF8/ySxhQXV5/G0Uzk+3h5b75Z24nrjnmfmvFXeh0nLFihMBXSsn5NJp5wJD9sq8kLX4zxOo4xlaKwKIpJMy6gVYPfOL3nSUC815HCghUKU2Gn92rPUQ2Vh2aeyw8bWnodx5jDNmXBMfy0pRk3DZ9FTLRdM7SfFQpTYSLCBZ1rUrtGMddMvpG8grhDz2RMmNqTH8+jH59Fz+YrOLbj5djX459sTZjDkhwnPHxaP37c3IwHp1efriFN5Hn+85PYsrsut4xcgIg1gunLk1NWROQhYBSQD/wEXKCqO0uZbjjwT5y+up9X1UkhDWoCMrBdYy7MSGHrV7XZu7IuiXsKIEUhMw/SC72OZ8whbc1J4ZlPT2Z4p3n0aH6r13HCjldbFLOBzqqaDqwCbik5gYhEA08CI4COwBkiUp2umq9Sbk5bz9/jnidxTyEgkB0F0xKdTl+MCXP7m+q4YfgmoIvXccKOJ4VCVWep6v6fmvMo/bLH3sBqVV2jqvnAZGB0qDKa8ombex8J5B84sECcTl+MCWM/b3Wa6jij98e0bnCH13HCUjgco7gQmFHK8KbAOp/H691hJhz568TFX6cvxoSJh2aeS1xMAddk1gCaeR0nLIkGqY9LEfkYKK2nm9tU9X13mtuAnsDJWiKIiJwKDFfVi93H5wB9VPUqP8sbD4wHSE1N7TF58uQK5c7JySEpKfz6iA73XH2/upiEfVsOGp8Xn8K8ftd4kCuNpKTw64HMcpVPsHOt3pnAffNaMKbNVsa0ScM5HBpIrvD+f6yIIUOGLFTVnqWOVFVPbsD5wFdADT/j+wEzfR7fAtwSyHP36NFDKyorK6vC8wZT2Of6/k3V+1JV76z1x23PxPr669wm6sVHLCvrYU+Wa7mqTq7iYvTUf/9Ne9z7qubk/UPLI+z/HysAWKB+VpYnu57cs5luBE5U1T1+JvsGaCsiLUUkDhgHTA1VRlNO6WNh1OOQ0gwQipLTmBRzLuO+up+tOSlepzPmIPub6rh22FRrquMQvDpG8QSQDMwWkUUi8jSAiDQRkekA6hzsvgqYCSwHpqjqMo/ymkCkj4XrlsJdO4n+6zJOveBWtubU5orXbqWgKLBNemNC4YCmOnqNwZrqKJtXZz21UdVmqtrNvV3mDt+gqiN9ppuuqu1UtbWq3u9FVlNxXdLq8fdTOzD/507cM22813GM+cNbC52mOm48bhax1lTHIYXDWU8mgo3u1p5LB9bilXnH88b847yOYwx78uN5ZPZZ9Gi+kuM6WVMdgbA1ZILuxuEDGNSumInvX86CtR28jmOquf1Nddw68htrqiNAVihM0EVHCY+PG07T2gVc9uptbNhZ3+tIppra31THcZ2+pkfzgxqEMH5YoTAhkVIjlufOPYa8ghpc+srt1tKs8cT+pjpuHL4RSPc6TpVhhcKETNvUFB49vTtLfmvDLf+9Gg3OtZ7GlGp/Ux3jes2xpjrKyQqFCaljOrbgr8fU593vhvD85yd5HcdUI3801TEsEWuqo3ysUJiQu2pob0Z2ER6ccQGfrjrK6zimGvj21/ZMXzKAS47+kIbJN3sdp8qxQmFCTkR46NRjaZeaz9Wv38jarY29jmQimCpMmn4B9ZN2csnALkBtryNVOVYojCdqxsfw3LnDiYqK4ZKXJ5KzL9HrSCZCfby8N/PXdubaYVNJsqY6KsQKhfFMs7o1eerMvqzZ2oTr3rye4mJrktxUrsKiKP720fm0qr+B03uNxprqqBgrFMZT/ds05fbjmzH7hz48NucMr+OYCPPWwmNYvfkIbhw+k9jocV7HqbKsn0rjufP7d+OHDVt5fM6ZdGz8M8M7f+V1JFOVLY6BOQlotjCYFVzT8C2O63QZ9ru44mzNGc+JCPedNJRuzfL5y5S/smJjc68jmapqcYzTV3t2FILQmB1MyH0fWbLd62RVmhUKExbiY6J55pwRJMUrl7w8kR25yV5HMlXRnASnr3Yf0UXFMOcejwJFBisUJmyk1krgmXMGsSm7Hle+fguFRfbxNOXkr492f326m4DYf6IJK92PaMD9J7Xly5/SeWD6hV7HMVVNip92YVLSQpsjwtjBbBN2TuvZkR9+38zWr+qT+0N9au7d53wBZOZBeqHX8UwYW51enyaf5VBD8v8cGJsImRO9CxUBbIvChKXbm23iofjnqbk3HxDIjnIOUi623zamdJt31+bMeXfzj/hTKa5VCxCnD/dRjzvd9JoKs/86E5ais+4lWvMPHFggzsHK9BxvQpmwVVgUxdWv38SuvCROvWIbUY1/wX4HVx4rFCY8+Tv46O9gpanWHpp1Ll//3IVHxj5Ph8YvYkWictnaNOHJz8HHwmT7yJoDfbS0H898eipn9ZnFyUfdAdTxOlLEsf86E54yJzoHIX3sJY5795zNL9saeRTKhJuftzbhhreuJT1tNRNHdQas2fpgsEJhwlP6WOcgZEoz9h+U3DZkEu/rYM54dhK/bkv1OqHx2N78eC5/9Raio4t56qylxMdc4nWkiOXJMQoReQgYBeQDPwEXqOrOUqZbC+wGioBCVe0ZypzGY+ljDzhbJQ14re1mznzuM854bhKTx99Es7qbvctnPKMKt717JSs3Nec/5z9HWp03vY4U0bzaopgNdFbVdGAVcEsZ0w5R1W5WJAxApyYNee3igeTsS2Lcs5NYv6OB15GMB16fP5z/fjeUazLfYXD7xwDrzySYPCkUqjpLVfdfOTUP58eiMQHp3LQhr150NLvzkhn37CR+22nFojr5fl1b7p56KYPafceEoacArbyOFPHC4RjFhcAMP+MUmCUiC0VkfAgzmTDXJS2VVy8ewK69taxYVCM7cpO54rVbaJC8k8dOzyUqapTXkaoFUfXTNsrhPrHIx0Bpp6fcpqrvu9PcBvQETtZSgohIU1X9TUQa4uyuulpVP/OzvPHAeIDU1NQekydPrlDunJwckpKSKjRvMFmu0q3JLuShb/aSFFvIzb1/pV5ioZsrjaSk8GsIznKVj2+uYoVHFqaxYlsNbu27hVYp3m1JeP259+dwcg0ZMmSh3138qurJDTgf+AqoEeD0dwHXBzJtjx49tKKysrIqPG8wWS7/vvt1g3ae+LYO/PtzumFnPVVFs7IeVo8+2mXeLFfFcz06+wxtftMH+uq8U1R1k3opHD73pTmcXMAC9fNGeLLrSUSGAzcCJ6rqHj/T1BSR5P33gWOBpaFLaaqKbs0a8/JF/diWU4cznp3Exux6XkcylWzuyqP455wzOPmouZzZ+y9AQ68jVSteHaN4AkgGZovIIhF5GkBEmojIdHeaVOALEfkemA98qKofeRPXhLvuRzThpQv7sjWnDmc89yA78qx1mkixfkcDrn3zetqnruP+MWmI9Pc6UrXjyX+TqrbxM3wDMNK9vwboGspcpmrr0bwpL13Yh3NfmM/f5tenf/+6pNayLjCrsoJi4YrXbqGoKJp/nz2PxLiXvI5ULYXDWU/GVJoezdN46cJe7NwXwxnPPcjmXdbuT1X2+vKGLF7fjofHvkrL+k8B1iikF6xQmIjTs0Uz/tIzgY3Z9Z1isbu215FMBbyzcChZ6+pw6aD3Oa7T34HwO8uourBCYSJSuzqx/N8FPfk9uwFnPvcgW6xYVCnLf2/Bbe9dQfs6e7jh2EzgSK8jVWtWKEzE6t3yCF48vye/7UjlzOceYGtOiteRTAB25dXg8ldvpVbCHi7vlkdM9OleR6r2rFCYiNa31RG8eP5RrNvRiDOfe5Dd82vBo0lwV7Lz17pWDSuqcMNb17J+R0OePOsdasdb6z7hwAqFiXj9WjfnxfO702XHGmKnxzr9b1s/3GHpuc9PYuay/twy8g16tXgSO3gdHuw/xFQL/Vu34KjkaSTkFhw4wvrh9t7iGJiTgGZHcbwuIrb5fzg/4wqgKfCj1+kMtkVhqpGE3I2lj7B+uL2zOMbZqsuOQoCmso3zt2UhS7Z6ncz4sEJhqg8//XBrSnAaxjQBmJPgbNX5kMJCmHOPR4FMaaxQmOqjlH6492gcjxSdal2rekSz/XwFZYdfS7bVmRUKU32U0g/3qt7X8X85Izn+8cf5YPEArxNWG6rw/Odj+E39NODoZ+vPeMMOZpvqpUQ/3N2A6f22MmHyB1z1+s38b/VHTDzhORLj9nmXMcLtzY/npneuZur3g5EjXuLC7XOc3U37xSY6W38mbNgWhan2mtWtz5RLz+WyQXm8MX84o598hFWbjvA6VkRatz2Vk//9ENMWD+SG4yZz4eUXIyf++4CtPEY9fkAxN96zLQpjgNjoKG4ecQr9Wi/iL2/u5sQnHuWuUc9weq9ZiJ0UVSk+/7EbV79xI8XFUfzn/GcZ3P5xoCWkY4UhzNkWhTE+BrXrxoxrRtKj+S5u/u8EJky+gd15iYee0filCk9/egrnvXg3qck7mXb1hwxu/ybQ0utoJkBWKIwpoWGtWrx84Xlcf2wx05cM4PjH/8Xi9aV2oWIOIXdfAle9cSOTZlzAiC5f898rcmle7yWghtfRTDlYoTCmFNFRwlVDRzF5fDsKixI45d8P8/zno1G75CJga7c25uSnHmbGkgxuGfE6T5wxlJrx12PNclQ9ViiMKUOvFkcy/ZqTGNx+J/d9eAkXvTSR7bm1vI4V9rJW9uDEJx5l0+56vHTh81w66AFEMr2OZSrICoUxh1C7Rg2ePedc7hoVyxc/dmfEP//FvDWdvY4VllThyazTuPD/7qRpna1Mu2omR7d9E2judTRzGOysJ2MCICKcn3EsPVv8zNVvfMGZzz3AhMw3mNDgHaI+iXPai0pRyMyD9MJDP2EEytmXyPVTruWjZRmM7vY5k05uRGLci9iupqrPCoUx5dC5aUumXd2UO96bwppPmpMfl0QCbmHIFqeBO/ZWu2KxZksTxr9yOz9vbcrtx7/CRQMuQ2Sw17FMJbFCYUw5JcXH8ejpZ5O7tg0Je0sUhGrYbPmc5b24dvL1xMYU8cpFz9O/9ZNAM69jmUpkhcKYCqq5t/SmsNVtMjti/dF/hLA7vgbv786keeNNPHPOIprWngIkeJ3QVDI7mG1MRflpuO43rcfFL93BZ6u6U1wcYSXjgP4jhFr79vJw/LP8d8D3NK39PFYkIpNnhUJE7hWRxSKySERmiUgTP9OdJyI/urfzQp3TGL9Kaba8OCaBRW2Hsmhde8598V4yH3maF784kV15kXGBWeHsmgf1HxGnhcTNnYcdtI5cXu56ekhV7wAQkQnAROAy3wlEpC5wJ9ATUGChiExV1R2hDmvMQfa3TzTnHqf/hJQ0ojInckL6WI4pzGXGkqm89FUB93wwnodnncNJ3bPoEBPnbeYK2Jhdjw8WD2Da94N4d9ddpdcD6z8ionlWKFR1l8/DmjiFoKTjgNmquh1ARGYDw4E3gp/QmACUaLZ8v/iYmozpfgZjuitL1n/Jy1+t4q2Fw8gvjGPahgc5r/8HHNNxHrHRRR6EPrTtubWYviSDad8PZP7aTqhG0bnpGnITEknet/fgGaz/iIgm6mGbBCJyP3AukA0MUdUtJcZfDySo6n3u4zuAvar6cCnPNR4YD5Camtpj8uTJFcqUk5NDUlJSheYNJstVPuGYa3d+AR+v2cMXG5VtebHUji9gSLOdDGq2k9rx3haMnJw0ohM28O2mJOb9Xotl22pSrELjmvvo2ziHPo2jaVSzDg03fUP7lU8SXfxnfx1FUfGsbH8lm1MHBSFX+L2PEJm5hgwZslBVe5Y2LqiFQkQ+BhqVMuo2VX3fZ7pbcArCnSXmD7hQ+OrZs6cuWLCgQpnnzp3L4MGDKzRvMFmu8gnnXEcPzCBrxYe89NUvfP5jG2KjCxjZ5X+c2+8DjspejcxJCNkFfHkFcXyyohcvfHwVS7bFk18YR1qdzYzq+iWj0mvSofEYRAZywOHMxVMO2N1G5sSgNRMezu9jpOUSEb+FIqi7nlR1WICTvgZMxzke4es3YLDP4zRg7mEHM8ZD0VGxDOs4hmEdYc2WRbwy71PeXtAbXRxDp7jnSKDAmbAyLuBzT2X1LTz5HeGL1d2Y9v1AZi3rS25+DVLiCzmz9yxO7KZ0bzYKkaeA2NKf08/uNhO5PDtGISJtVfVH9+FoYEUpk80EHhCROu7jY4FbQpHPmFBo1aAbd47qxvXHbkcfvYGEvIIDJygQNr7bhEs+vY5aibkkx+c6fxP2kJyQS62EXOdvYu4fj51he6j14z6iP4z/8yylbCH/3WTu/O+5vJF3DCmJOZzY7X+MSs8hb90JDB3yMGB9b5iDeXnW0yQRaQ8UA7/gnvEkIj2By1T1YlXdLiL3At+489yz/8C2MZGkZnxdyNtZ6rhU3Um9pN3szktk86667M6rye68GuTml/2l/kXcBNKiDrwoME6LuCHmLY45P5sBbTKJi7kXSGbu+rlYkTD+eHnW0yl+hi8ALvZ5/CLwYqhyGeOZlDTIXnfQYElpxv9dcAfOiYE5OOd+ZFNYtIOcfdns2ruLXXm57M7by668PezOy2V3XgFNZ5d+5XjdwlyGHvmfYL4SE2GsCQ9jwkXmRJg2AQp8Tj+NTXSGA84FDMnuLY2YaKhdw7mVav60UguPncpqysua8DAmXKSPhVGPQ0ozQJy/ox6v+IHjUq4cP7DwGBMY26IwJpxU5hlFpVw5HsxTWU3kskJhTCSzU1lNJbBdT8YYY8pkhcIYY0yZrFAYY4wpkxUKY4wxZbJCYYwxpkyeNjMeLCKyBadZkIqoD5R+Sau3LFf5WK7ysVzlE4m5mqtqg9JGRGShOBwissBfU7teslzlY7nKx3KVT3XLZbuejDHGlMkKhTHGmDJZoTjYs14H8MNylY/lKh/LVT7VKpcdozDGGFMm26IwxhhTpmpRKESkmYhkicgPIrJMRK4pZRoRkcdFZLWILBaRo3zGnSciP7q380Kc6yw3zxIR+VJEuvqMW+sOXyQiCyorVzmyDRaRbHf5i0Rkos+44SKy0l2fN4cw0w0+eZaKSJGI1HXHBXN9JYjIfBH53s12dynTxIvIm+46+VpEWviMu8UdvlJEjgtxrr+463SxiMwRkeY+44p81ufUEOc6X0S2+Cz/Yp9xwfqfDCTXoz6ZVonITp9xQVlfPs8fLSLficgHpYwL3udLVSP+BjQGjnLvJwOrgI4lphkJzMDpHaYv8LU7vC6wxv1bx71fJ4S5+u9fHjBify738VqgvofrbDDwQSnzRgM/Aa2AOOD7kvMGK1OJ6UcBn4RofQmQ5N6PBb4G+paY5grgaff+OOBN935Hdx3FAy3ddRcdwlxDgBru/cv353If53i4vs4Hnihl3mD+Tx4yV4nprwZeDPb68nn+vwCv+/m/C9rnq1psUajq76r6rXt/N7AcaFpistHAy+qYB9QWkcbAccBsVd2uqjuA2cDwUOVS1S/d5QLMA0LSPVmA68yf3sBqVV2jqvnAZJz1G+pMZwBvHO5yA8ymqprjPox1byUPAI4GXnLvvw1kioi4wyer6j5V/RlYjbMOQ5JLVbNUdY/7MCSfsQDXlz/B/J8sb66QfcZEJA04HnjezyRB+3xVi0Lhy90c647zS8FXU8C338j17jB/w0OVy9dFOFs9+ykwS0QWisj4ys4UYLZ+7mb6DBHp5A4L+jo71PoSkRo4Xx7v+AwO6vpydwssAjbjfJH5/YypaiFO59f1CPL6CiCXr5KfsQQRWSAi80RkTGVlKkeuU9xdYm+LSDN3WFisL3cXXUvgE5/BQVtfwGPAjUCxn/FB+3xVq0IhIkk4XxzXquour/PsF0guERmC8098k8/gAap6FM4uqStFZGCIs32Lc9l/V+BfwHuVvfwKZNpvFPA/Vd3uMyyo60tVi1S1G84v8t4i0rkyn7+iAs0lImcDPYGHfAY3V+dK3zOBx0SkdQhzTQNaqGo6zlbDSyWfIxjK8T6OA95W1SKfYUFZXyJyArBZVRdWxvOVV7UpFCISi/Pl8pqq/reUSX4Dmvk8TnOH+RseqlyISDrO5uZoVd22f7iq/ub+3Qy8SyXtrgg0m6ru2r+ZrqrTgVgRqU8Q11kg68s1jhK7BIK9vnyWsxPI4uDdIX+sFxGJAVKAbQT5MxZALkRkGHAbcKKq7vOZZ/86WwPMxdmKC0kuVd3mk+V5oId73/P15SrrM1bZ6ysDOFFE1uLsyh0qIq+WmCZ4n6/yHNCoqjecA1QvA4+VMc3xHHgwe747vC7wM85Bszru/bohzHUEzj7F/iWG1wSSfe5/CQwP8TprxJ/X4vQGfnXni8E5wNiSPw9mdwpFJne6FGA7UDOE66sBUNu9nwh8DpxQYporOfBg4xT3ficOPNi4hso7mB1Iru44BzjblhheB4h379cHfqQSTkooR67GPvdPAua594P5P3nIXO64I3FOjpBQrK8Syx5M6Qezg/b5qi59ZmcA5wBL3H2PALfifAmjqk8D03HOfFoN7AEucMdtF5F7gW/c+e7RA3dnBDvXRJz9jE85x6UoVGfTNhV41x0WA7yuqh9VUq5As50KXC4ihcBeYJw6n8xCEbkKmIlzBtSLqrosRJnA+VKZpaq5PvMGe301Bl4SkWicLfUpqvqBiNwDLFDVqcALwCsishqnkI1zcy8TkSnAD0AhcKUeuDsj2LkeApKAt9z186uqngh0AJ4RkWJ33kmq+kMIc00QkRNx1sl2nLOggv0/GUgucN67ye7nfb9grq9SherzZVdmG2OMKVO1OUZhjDGmYqxQGGOMKZMVCmOMMWWyQmGMMaZMViiMMcaUyQqFMcaYMlmhMMYYUyYrFMYEmYj0chu2SxCRmm4/B2HRDpQxgbAL7owJARG5D0jAaRZivao+6HEkYwJmhcKYEBCROJwmJ/Jw2u2qrCY6jAk62/VkTGjUw2lPKRlny8KYKsO2KIwJAbf/5Mk4rXc2VtWrPI5kTMCqS+uxxnhGRM4FClT1dbdV0i9FZKiqfnKoeY0JB7ZFYYwxpkx2jMIYY0yZrFAYY4wpkxUKY4wxZbJCYYwxpkxWKIwxxpTJCoUxxpgyWaEwxhhTJisUxhhjyvT/M9LnLNSIjTAAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(np.linspace(0, 15, 15 + 1) * 0.133333 + 2, f(np.linspace(0, 15, 15 + 1) * 0.133333 + 2))\n",
        "plt.plot(np.linspace(0, 15, 15 + 1) * 0.133333 + 2, f(np.linspace(0, 15, 15 + 1) * 0.133333 + 2), 'o')\n",
        "\n",
        "plt.fill_between(np.linspace(0, 15, 15 + 1) * 0.133333 + 2, f(np.linspace(0, 15, 15 + 1) * 0.133333 + 2), color='yellow')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('f(x)')\n",
        "plt.title('Integral 2 - Área: Simpson 3/8')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CkX3q0TS1Q-p"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 7. Integración - Integral 2 - Área: Simpson 3/8\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "Xd1_MN0ZS5qR",
        "outputId": "5364d1fe-2571-4626-a7aa-83add56a44af"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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89tpr1WXvu+8++vfvz7e+9S3WrVtXPX/VqlWMGDGCQYMGcfHFF7N79+642+zE6YeHgLGq6heRNOBdEfmnqibFxU98KT6mj57Olf+4kpuLb2bueXPpkdnD7bCMaZ7+eTts+9jZOrsOhG9Pj6loIBDgnXfe4ZprrgFCP8v/3e9+R79+/Vi6dCk33HADCxYs4J577uGNN96gR48eDRqGmT59OqtXr2bVqlUAVFZW8sorr9CmTRtKSkoYMWIEF1xwAStXrmTevHmsWrWKyspKhg4dyrBhwwC46qqrePzxxznjjDOYOnUqd999NzNnzmzgTqnJiZsvq6r6w5Np4UdSXVc2Kz2LWYWzqAxWMnnBZA5UJP52T8aYpnPw4EHy8vLo2rUr27dv56yzzsLv9/Pvf/+bSy+9lLy8PK677jq2bt0KwKhRo5g4cSJ/+MMf4roLkKryq1/9ikGDBnHmmWfy9ddfs337dhYvXszFF19Mq1ataNOmDRdccAEAe/fuZc+ePdUXz3Lq0raO/CBIRHzACqAv8KSqLo1SZhIwCSA7O7vOR5am8IP2P+Dpb57mulev40edfkSK1H8c8/v9rsTotObSDrC2JCO/30/btm0PXwL2W3cmZkMRl5iNpmXLlixevJgDBw5w8cUX8/DDD3PllVfStm1bFi9eXKuqUmbMmMGyZct44403GDp0KAsXLkREKCsrq27L/v37OXDgAKWlpagqfr8fv99PMBisLjNnzhy2bt1KcXExaWlp5ObmUlJSQllZGYcOHaouV15eXj2tqtXza9cXqaysLPb3iKo69gDaAUVA7pHKDRs2TN3y3OrnNPe5XH1q1VNHLFdUVNQ0ASVYc2mHqrUlGRUVFeknn3zidhjaunXr6tcrV67U4447TisqKnTkyJH6l7/8RVVVg8Ggrlq1SlVVP/vss+ry+fn5+uGHH+obb7yhI0eO1EAgoF9++aVmZWVV/52OP/543bFjh5aUlOhxxx1Xve7MmTP1xhtvVFXVBQsWKKAbN27UFStW6MCBA/XAgQO6b98+7du3r86YMUNVVQcNGqSLFi1SVdVf//rXOmXKlKhtirZfgeUaJac6+hN9Vd0jIkXAOcBqJ+t2ylUnX8W6Xet4atVT9G/Xn3HHj3M7JGOMg4YMGcKgQYOYO3cuc+bM4Sc/+Qn33nsvFRUVjB8/nsGDB3PrrbeyYcMGVJVx48YxePBgSktL6d27NyeffDInnXQSQ4cOrVN3x44dGTVqFLm5uXz729/mtttu4/zzz2fgwIHk5+dz4oknAjB06FAuv/xyBg8eTJcuXWpc5vb555/n+uuv58CBA5xwwgk8++yz8Tc6WnZvyAPoDLQLv24JLAbOO9I6bvbIVVXLKst0wvwJeuoLp+q6XeuilmlOPabmwtqSfJKlR+6Effv2uR1CDQ3pkTtxHnk3oEhEPgKWAW+p6nwH6k2YFr4WzCycSWZaJpMXTGZ3Wfyn/xhjjFucOGvlI1UdoqqDVDVXVe9xIrBE69KqCzMLZ7LjwA5uWXgLFUH7Gb8xxpua9S87j2ZQ50H8+vRf88G2D5ixbIbb4RhjTKM0q+uRN8YFfS5g3a51/OmTPzGg/QC+2/+7bodkjDENckz3yKvcNOwmTu9+OvcuvZeV21e6HY4xxjSIJXIgNSWVB8c8SI/MHtxUfBNb/VvdDskYY2JmiTysbYu2zCqcxaHAIX5e9HPKg+Vuh2SMiVHVZWyrHtOnx3ZtlubimB8jj3RCuxN4cMyD3PjOjcwpm8NZehYi4nZYxpijqLqM7ZEEAgF8Pl+907Gul4ysR17LmJ5jmDx0MisPrOSZ1c+4HY4xJg45OTncdtttDB06lJdeeqnO9Ny5cxk4cCC5ublMnTq1er3MzExuvvlmBg8ezJIlS1xsQWysRx7FNbnX8O6n7zJr5Sz6tutLQa8Ct0MyxhMe+OABx296fmKHE7nttNuOWKbq6odV7rjjDi6//HIg9LP6lStDJzHcfvvt1dNbtmxhxIgRrFixgvbt2zNu3DheffVVLrroIvbv38/w4cN5+OGHHW1Lolgij0JEuKLjFRzIOMDti29nzrlz6NOuj9thGWPqcaShlaqEXnt62bJlFBQU0LlzZwAuu+wyFi1axEUXXYTP5+O73/XOqciWyOuRnpLOrLGzGD9/PJMXTOZ/v/O/tG3R1u2wjElqR+s5u6F169ZHnI4mIyMj6cfFI9kY+RF0bd2VRwsfZcv+Ldy68FYqg5Vuh2SMcchpp53GwoULKSkpIRAI8PLLL1ff8MFrLJEfxZAuQ7hrxF0s2bqER1Y84nY4xpgoqsbIqx633377Udfp1q0b06dPp7CwkMGDB5OXl8eFF17YBNE6z4ZWYnBJv0tYt2sdf/7kzwxoP4AL+3rzj21Mc1Xf7do2bdp0xOkJEyYwYcIEgBp36fH7/XiJ9chjdMuptzC863DuXnI3/9nxH7fDMcaYapbIY5SWksZDZzxEdqtsphRNYfv+7W6HZIwxgCXyBmmX0Y5ZY2dxoOIAU4qmUFZZ5nZIxiSF0M1rjFMauj8tkTdQv/b9uH/0/azeuZq7l9xtb2BzzMvIyGDnzp32b8EhqsrOnTvJyMiIeZ24v+wUkV7An4BsQIHZqvpYvPUms7HHjeWneT/lyVVPMqD9ACbmTnQ7JGNc07NnTzZv3syOHTvcDiUuZWVlDUqeiZSRkUHPnj1jLu/EWSuVwM2qulJEsoAVIvKWqn7iQN1J67pB17F+93oeXfkofdv35Vs9vuV2SMa4Ii0tjd69e7sdRtyKi4sZMmSI22E0ihP37NyqqivDr0uBtUCPeOtNdiLCvaPupV+7fvxy4S/ZuHej2yEZY45R4uS4lojkAIuAXFXdV2vZJGASQHZ29rB58+Y5tt1E8Pv9ZGZmHrXcrspdzNg6g1Yprbil2y20TGnZBNHFLtZ2eIG1Jfk0l3aAN9pSWFi4QlXz6yxQVUceQCawArjkaGWHDRumya6oqCjmssu2LtO85/P0+reu18pAZeKCaoSGtCPZWVuST3Nph6o32gIs1yg51ZGzVkQkDfh/wBxV/asTdXpJftd87hh+B+9+/S6Pfdisv+c1xiQhJ85aEeAZYK2qHrMXI7lswGWs27WOZ1c/S//2/TnvhPPcDskYc4xwokc+CvgBMFZEVoUf5zpQr+fcftrtDMsexrR/T2NNyRq3wzHGHCOcOGvlXVUVVR2kqnnhxz+cCM5r0nxpPFLwCB0zOjK5aDI7Dnj7vFpjjDfYLzsd1iGjA7PGzqK0vJSbim+iPFDudkjGmGbOEnkCDOgwgHtH3ct/dvyH37z/G/vpsjEmoSyRJ8h/5fwX1w26jlc/e5U5a+e4HY4xphmzRJ5AN+TdwNheY3lo+UMs2bLE7XCMMc2UJfIESpEUfjv6t/Ru25tbFt7Cl/u+dDskY0wzZIk8wVqntWbW2FmICJMXTMZf7q1bSBljkp8l8ibQK6sXD5/xMJv2beKOxXcQ1KDbIRljmhFL5E1keLfh3HrqrRRvLuaJD59wOxxjTDPixPXITYyuOPEK1u9ezx8+/gP9O/TnnJxz3A7JGNMMWI+8CYkIdw6/k7zOedz17l2s3bnW7ZCMMc2AJfImlu5L59HCR2nboi2Tiyaz8+BOt0MyxnicJXIXdGrZicfGPsbust38ovgXVAQq3A7JGONhlshdckrHU7jn9HtY+c1KfvvBb+1n/MaYRrMvO1107gnnsn73ep5Z/QwD2g9g/Inj3Q7JGONB1iN32c+G/IwxPcfwwAcPsGzbMrfDMcZ4kCVyl/lSfEwfPZ1ebXrxi+JfsLl0s9shGWM8xql7dv6PiHwjIqudqO9Yk5WexeNjHyegASYXTeZAxQG3QzLGeIhTPfLnAPt1SxyOb3M8D415iM/3fM6d795pP+M3xsTMkUSuqouAXU7UdSw7vcfp/GLYL3j7y7f5/X9+73Y4xhiPEKdOexORHGC+qubWs3wSMAkgOzt72Lx58xzZbqL4/X4yMzObfLuqygs7X+CD/R9wTedryGuVF1d9brUjEawtyae5tAO80ZbCwsIVqppfZ4GqOvIAcoDVsZQdNmyYJruioiLXtl1WWaZXzL9CT33hVF23a11cdbnZDqdZW5JPc2mHqjfaAizXKDnVzlpJQi18LXi08FEy0zKZvGAyu8t2ux2SMSaJWSJPUl1adeGxwsfYcWAHNy+8mYqg/YzfGBOdU6cfzgWWAANEZLOIXONEvce6gZ0HMu30aSzbtowHP3jQ7XCMMUnKkZ/oq+oEJ+oxdZ3f53zW717Pc2ueY0CHAXyv//fcDskYk2Q8M7Sy9/XX2TB2HGtPOpkNY8ex9/XX3Q6pyUwZOoVRPUZx39L7WLl9pdvhGGOSjCcS+d7XX2frXVOp3LIFVKncsoWtd009ZpK5L8XHg2MepGdmT24qvomt/q1uh2SMSSKeuPrhN4/ORMvKaszTsjI+vns6T2/vTNc2LenWNoNu7TJCz21D021bpiEiLkXtrDbpbZg1dhZX/P0Kfl70c57/9vO0TG3pdljGmCTgiUReuTV6D7SDfxcHywMs+byE7aWHCARr/ripZZqvOsE3h2Tfu21vHhjzADe+cyNT35vKg2Me9EzsxpjE8UQiT+3WLTSsUkta9+789YZRAASCyo7SQ2zde5Cte8tCjz0H2bov9NzQZL/jm0qyt+5LumQ/pucYpgybwqMrHqV/+/5cO+hat0MyxrjME4m8y01T2HrX1BrDK5KRQZebplRP+1KErm0z6No2gyH11FOV7LfsPci2GJL9zJWLgeTr2f/olB+xfvd6Hv/wcfq170dBr4Im2a4xJjl5IpG3Pf98IDRWXrl1K6ndutHlpinV82MVmezrU5Xs5xe9R/c+J8fds09EshcRpo2cxqa9m7h98e3MOXcOfdr1ibteY4w3eSKRQyiZNzRxN0ZVsu/bzkfBwG5Ry1QGgpT4y6t79lv2hHv4TZjsM1IzmFk4k/Hzx/OzBT9j7nfm0rZFW0f2gTHGWzyTyJNJqi/lqD37epP93jK27nUm2Xdt3ZWZhTO5+o2ruWXhLTx95tOkpoT+pHtff51vHp1Jly1b2NC9e6M+wRhjvMESeYI4kez//XkJ2/eVUSvX10n2p2Zey7+3PsWUt37DTwfdTNv33mHfvfegZWUIVJ93D1gyN6YZskTuIueS/XGkdRnFQv7Kv1am8Me//IvsKOfdr7v3QV6pOJ4WqT5apvvISPXRMj2FjDRf9aNlmo+MtJTwc9Wj5rQvJTnO4DHGhFgiT3KxJvtt+8Zwy+LJfCqv0eXgwajlMveW8PbabyirCHCoIkh5oHG3k0v3pZCRFjoAVB0QqqZrHAzSfZ45aFQNRcXzZboxbrFE3gyk+lLo2T6L3589kwl/n8Cutl/QcW/dJJ3WvTvL7jyzejoQVMoqAhysCFBW/QhWTx8sD1BWGaSsPEBZZXg6YnnV42DEensOlLO1om65ikDj7kQVedDQynI6fLjI8YNG5Zv/Yvc906pPb7WhqKOz72CSiyXyZqRti7bMKpzF4x9cyrcXp/J5lw6UpaWSUVHJiSWl5Eecdw+hM3Rat0ildYvEvw0qA8HQQSF8gDhU2fCDxhebt9CmQyvHDxrPvTE96lDUR9Pu5861maSmCKk+ITUlhTSf4EsRUn2h16kpKYeX+1JISxF84XKpNZZHlPcJX2wq5/PUjdX1pYXnp/rC5VOENF9onq/qdfg5NH24rqrnqjp8EeUSoeraR/YdTMMk8lOfJfJmpm/7vowecS0fb5pPioauiVaWnsbHvbrQvV0mbp2gmOpLIdOXQmYcB43i4l0UFNS9XWFt0Q4aB8uDEQeImgeNLq/ujVpPx/17GHpcOyqDSmVAqQwGqQgogaBSEQhSVhGkMlBZvbwiGKQyYnll+DkQsbzGLXLXfdLofRELEcIHhXCirzoIhA8soYPA4QNUaq2DRI2DVsrhg8x3ZzxIZpQD3+e/ncF7rU4kJUVIEcGXQvg59BARfDHOr65DhJQUwstD830SWpaSEuqMhMrEPr962yKI0CQ/5Is8+IHzBz9L5M3QrreWVSfxKoFAJQvmPENabi9apLYgw5dBi9QWtPC1ID0lPWkuQeCEhh40Nj4P/ZAAAA+ESURBVHSv7xIQ3Zg5vr7fCTdOIBg6IBQVL2Lk6d+iIhg8nPgDGjoohA8IVQeBisDheaGDRpCK8HPdg0zouWpedfnwdHV94ToCEetWbaPqAFV90Kp1gLpqT0nUtrXYvYOH31rv6P5qCikSSvCokrbgX9UJvupAU31wiTioVB0g6pt/+Dl0cPrp7x+gbZSD3zePzkyeRC4i5wCPAT7gj6o63Yl6TeOU7oz+D+3g7t1c/LeL68wXhBa+FtWJvepRlewzfBmk+9JrJP/qMqkZ1WXTfek1piPLRls3WQ4eXW6awvIH7+fTTllHHIpyQig5+MhIFdq2SnO8/qaw4Z3ufHFgH+u6HR66G7B1F8e3zOKz+75NQJVgEAIaSv7BoBJUrTE/GAwtC4RvHhwIhg5yQW3c/KBWvSZUd+T8oBLQWvODSlAjYlFl0xdf0qNHT4JKje1VxVr//HBdkXGGD8jBQGh+m307+bpdZp191qOeCwI2VNyJXER8wJPAWcBmYJmI/E1VE/u50dQrq2MnSkt21Jmf3q4NM86YwaHKQxwKHKKssoxDgUPVj6rpskAZ5YFyygJlHKo8xL7yfXXKVL1WGvclJlAjyUceBKoOENUHj/D0N7u+4aOVH9U4gFQ/qj5lRJmuqquFrwUpUvcS/FvaZfJxry4EApVAcgxFJbN9F32H1YvfJpByeOhuda/OtB99Zmj4xeX4Gqu4eBsFBScnpO6i+b34ODOVYErkcGdnfO3bc5ID9Tuxz08DPlPV/wMQkXnAhYAlcpeMHn8Vb85+gsryQ9XzUtNbcNb3J3FSTqFj21FVKoOVoYQfTuzVB4AjHCiqH5WHqsvWnvaX+w+vFz6g7C/fz8LVCwlq406bBEhPSa/zKeO0vwVoUesL0kCgkr899xi/q3gVEUGQ6k8QVa+r/gv9X3Ne1LLhZ4BtO7exaMmiqMsjy9Wus8b26isbLbZa9UdrR30x1563bfXS6iRevb9SUli8eikb179cXb622p/AopWJJtont0TUv9a/Fv//+euvv9a8WONCYEOXTIJl5TVmB1NSWN+tA078i3QikfcAvoqY3gwMr11IRCYBkwCys7MpLi52YNOJ4/f7kz7G+gk9R49jy9J3KffvIz2zDd2Hf4vtAWG7C21qEf6vDW2OXFAIvSNTgRZ1F/v9fjIzMwlogHItp0Iraj6CFXXn1fMo13IqtZKKigrS9++OGo7PX8Gn2z6t/tRR/axad17Es+oRloVfB4NBPvrso+p5Ncpq9HUit1/vsjg+IcXqh3uPi5qwKvf6uXvJ3QnffkItTky1PyyLvs/8+53JM032KUhVZwOzAfLz87WgoKCpNt0oxcXFJHuMR1RQAJNu8H47IiSqLbOLfxR1KKpNpy68ccWzjm8PEv/+qjrYVD9HHCBqzNeaB6DI5TXqiVj+8tKb2b9zZ51tZnbsxNvf+5+YDiZV9deYF2W9qPNiWTdKCEerf+nSpQwfPjym+qO28QjbfOP9aRzcVbfDkNWpsyPvAycS+ddAr4jpnuF5xnhCfUNRo8df5WJU8YkchnHaGRMmRt1fZ0yYSHbrbOc32EQ2pm3k+DbHJ6TuwiuuTuh7zIlEvgzoJyK9CSXw8cAVDtRrTJM4aXRolHLxvD9RurOErI6dGD3+qur5pqYa+6tkB1mdOtv+OopEv8fiTuSqWikiNwJvEDr98H9UdU3ckRnThE4aXWiJqAGq9ldzGrpLtES+xxwZI1fVfwD/cKIuY4wxDVP3pFpjjDGeYoncGGM8zhK5McZ4nCVyY4zxOEvkxhjjcZbIjTHG4yyRG2OMx1kiN8YYj7NEbowxHmeJ3BhjPM4SuTHGeJwlcmOM8ThL5MYY43GWyI0xxuMskRtjjMdZIjfGGI+zRG6MMR4XVyIXkUtFZI2IBEUk36mgjDHGxC7eHvlq4BJgkQOxGGOMaYS47tmpqmsBRMSZaIwxxjSYqGr8lYgUA7eo6vIjlJkETALIzs4eNm/evLi3m0h+v5/MzEy3w4hbc2kHWFuSUXNpB3ijLYWFhStUtc4w9lF75CLyNtA1yqI7VfW1WANQ1dnAbID8/HwtKCiIdVVXFBcXk+wxxqK5tAOsLcmoubQDvN2WoyZyVT2zKQIxxhjTOHb6oTHGeFy8px9eLCKbgZHA30XkDWfCMsYYE6t4z1p5BXjFoViMMcY0gg2tGGOMx1kiN8YYj7NEbowxHmeJ3BhjPM4SuTHGeJwlcmOM8ThL5MYY43GWyI0xxuMskRtjjMdZIjfGGI+zRG6MMR5nidwYYzzOErkxxnicJXJjjPE4S+TGGONxlsiNMcbj4r1D0AwR+VREPhKRV0SknVOBGWOMiU28PfK3gFxVHQSsB+6IPyRjjDENEVciV9U3VbUyPPk+0DP+kIwxxjSEqKozFYm8Dryoqi/Us3wSMAkgOzt72Lx58xzZbqL4/X4yMzPdDiNuzaUdYG1JRs2lHeCNthQWFq5Q1fza84+ayEXkbaBrlEV3qupr4TJ3AvnAJRrDkSE/P1+XL18eU+BuKS4upqCgwO0w4tZc2gHWlmTUXNoB3miLiERN5KlHW1FVzzxKxROB84BxsSRxY4wxzjpqIj8SETkH+CVwhqoecCYkY4wxDRHvWStPAFnAWyKySkR+50BMxhhjGiCuHrmq9nUqEGOMMY1jv+w0xhiPs0RujDEeZ4ncGGM8zhK5McZ4nCVyY4zxOEvkxhjjcZbIjTHG4yyRG2OMx1kiN8YYj7NEbowxHmeJ3BhjPM4SuTHGeJwlcmOM8ThL5MYY43GWyI0xxuMskRtjjMfFlchF5Dci8lH47kBvikh3pwIzxhgTm3h75DNUdZCq5gHzgakOxGSMMaYB4krkqrovYrI1oPGFY4wxpqHiumcngIjcB1wF7AUK447IGGNMg4jqkTvRIvI20DXKojtV9bWIcncAGar663rqmQRMAsjOzh42b968RgfdFPx+P5mZmW6HEbfm0g6wtiSj5tIO8EZbCgsLV6hqfp0FqurIAzgOWB1L2WHDhmmyKyoqcjsERzSXdqhaW5JRc2mHqjfaAizXKDk13rNW+kVMXgh8Gk99xhhjGi7eMfLpIjIACAJfANfHH5IxxpiGiCuRq+p3nQrEGGNM49gvO40xxuMskRtjjMdZIjfGGI+zRG6MMR5nidwYYzzOErkxxnicJXJjjPE4S+TGGONxlsiNMcbjLJEbY4zHWSI3xhiPs0RujDEeZ4ncGGM8zhK5McZ4nCVyY4zxOEvkxhjjcZbIjTHG4+K91RsAInIz8BDQWVVLnKiztvVLt7Hktc/x7zpEZocWjLywD/2Hd03EppqFw/sryBdvvmf76yjs/dUw9v5quES+x+JO5CLSC/gv4Mv4w4lu/dJtFM35lMryIAD+XYcomhO6z7O9eeqy/dUwtr8axvZXwyV6nznRI38U+CXwmgN1RbXktc+rd0CVyvIgS+Ysof8nf0zINvP27IGN7RJSd6It+fDHVJa3rTEv0furKSTqb+LG/rL3V/JJ5N+k3n322ufuJ3IRuRD4WlX/IyJHKzsJmASQnZ1NcXFxzNvx7wpGn1/ehj179sRcT0MEAoGE1Z1o/vI29c73apsgcX8TN/aXvb+STyL/JvXus12HGpQL63PURC4ibwPRDhl3Ar8iNKxyVKo6G5gNkJ+frwUFBTEH+cWb7+HfdajO/MwOGbS76b2Y62mI4uJiGhJjMsn8VdPvr6aQqL+JG/vL3l/JJ5F/k/r3WQsKCkbFXf9Rz1pR1TNVNbf2A/g/oDfwHxHZBPQEVoqI44NkIy/sQ2p6zVBT01MYeWEfpzfVLNj+ahjbXw1j+6vhEr3PGj20oqofA12qpsPJPD8RZ61UjSHZWQWxsf3VMLa/Gsb2V8Mlep85cvphU+g/vKu9URqgan+FPi7G/9GtubP3V8PY+6vhEvkecyyRq2qOU3UZY4yJnf2y0xhjPM4SuTHGeJwlcmOM8ThL5MYY43Giqk2/UZEdwBdNvuGG6QQk5AJgTay5tAOsLcmoubQDvNGW41W1c+2ZriRyLxCR5aqa73Yc8Wou7QBrSzJqLu0Ab7fFhlaMMcbjLJEbY4zHWSKv32y3A3BIc2kHWFuSUXNpB3i4LTZGbowxHmc9cmOM8ThL5MYY43GWyKMQEZ+IfCgi892OJR4i0k5EXhaRT0VkrYiMdDumxhCRm0RkjYisFpG5IpLhdkwNISL/IyLfiMjqiHkdROQtEdkQfm7vZoyxqKcdM8Lvr49E5BUR8cT966K1JWLZzSKiItLJjdgawxJ5dD8H1rodhAMeA/6lqicCg/Fgm0SkBzCZ0LXucwEfMN7dqBrsOeCcWvNuB95R1X7AO+HpZPccddvxFpCrqoOA9cAdTR1UIz1H3bY0yc3kE8ESeS0i0hP4DuDdu8gCItIWGAM8A6Cq5arq1RsqpgItRSQVaAVscTmeBlHVRcCuWrMvBJ4Pv34euKhJg2qEaO1Q1TdVtTI8+T6hO4UlvXr+JnD4ZvKeOgvEEnldMwn9IaPf8dk7egM7gGfDw0R/FJHWbgfVUKr6NfAQoR7SVmCvqr7pblSOyFbVreHX24BsN4NxyNXAP90OorEibybvdiwNZYk8goicB3yjqivcjsUBqcBQ4GlVHQLsxxsf32sIjx1fSOjA1B1oLSLfdzcqZ2noHGBP9QBrE5E7gUpgjtuxNIaItCJ0M/mpbsfSGJbIaxoFXBC+/+g8YKyIvOBuSI22GdisqkvD0y8TSuxecyawUVV3qGoF8FfgdJdjcsJ2EekGEH7+xuV4Gk1EJgLnAVeqd3+Y0ocmupl8Ilgij6Cqd6hqz/Bt68YDC1TVk70/Vd0GfCUiA8KzxgGfuBhSY30JjBCRViIihNrhuS9to/gb8MPw6x8Cr7kYS6OJyDmEhiIvUNUDbsfTWKr6sap2UdWc8L//zcDQ8L+jpGeJvHn7GTBHRD4C8oDfuhxPg4U/UbwMrAQ+JvSe9dRPqUVkLrAEGCAim0XkGmA6cJaIbCD0qWO6mzHGop52PAFkAW+JyCoR+Z2rQcaonrZ4lv1E3xhjPM565MYY43GWyI0xxuMskRtjjMdZIjfGGI+zRG6MMR5nidwYYzzOErkxxnicJXJjABHJCV+z/Q/ha5+/KSIt3Y7LmFhYIjfmsH7Ak6p6CrAH+K7L8RgTE0vkxhy2UVVXhV+vAHJcjMWYmFkiN+awQxGvA4QuBWxM0rNEbowxHmeJ3BhjPM6ufmiMMR5nPXJjjPE4S+TGGONxlsiNMcbjLJEbY4zHWSI3xhiPs0RujDEeZ4ncGGM87v8D9Whcxunc5tgAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(list(map(lambda x: x[0], np.array(table2, dtype=np.int8))), list(map(lambda x: x[1], np.array(table2, dtype=np.float64))), label='Intervalo')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table2, dtype=np.int8))), list(map(lambda x: x[2], np.array(table2, dtype=np.float64))), label='Resultado')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table2, dtype=np.int8))), list(map(lambda x: x[3], np.array(table2, dtype=np.float64))), label='Error')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table2, dtype=np.int8))), list(map(lambda x: x[1], np.array(table2, dtype=np.float64))), 'o')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table2, dtype=np.int8))), list(map(lambda x: x[2], np.array(table2, dtype=np.float64))), 'o')\n",
        "plt.plot(list(map(lambda x: x[0], np.array(table2, dtype=np.int8))), list(map(lambda x: x[3], np.array(table2, dtype=np.float64))), 'o')\n",
        "\n",
        "plt.xlabel('n')\n",
        "plt.title('Integral 2: Simpson 3/8')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "siDsAs7n1cIe"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 8. Integración - Resultados segunda integral\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lNYZn407irEc"
      },
      "source": [
        "## 5. Conclusiones\n",
        "La **derivación numérica** nos permite dar una aproximación cercana a lo esperado, respecto a una función dada, además de este método poder resolver derivadas que de otra forma no se podrían resolver, llegando así a dar resultados necesearios del fenómemo al cual se vaya implementar; este método nos refleja una aproximación precisa, a exepción de los extremos de dos puntos, a los cuales si se desea tener un mejor resultado se debe de ampliar los datos o puntos de aproximación a emplear en el fenómeno\n",
        "\n",
        " \n",
        "En la integración nos permite abarcar resultados mas aproximados gracias al método de **Simpson $\\frac{3}{8}$**, permitiendo resolver integrales definidas de forma numérica, aprovechando este método para los fenómemos que se puedan implementar a nivel computacional, gracias a su rápida convergencia, sin perjudicar la tasa de error.\n",
        "\n",
        "\n",
        "La derivación e integracion numpérica nos concluye las dos diferentes formas de plasmar la aproximación del resultado de una función dada que nos permite resolver un problema numéricamente, además de facilitarnos la graficacion de esta, olos detalles y acciomas que se puedan presentar en el fenómeno dado."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ggip3qvriwBl"
      },
      "source": [
        "## 6. Referencias"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZrhJPErCTYzN"
      },
      "source": [
        "- [Matemáticas Básicas. Aplicaciones de la Integral](http://132.248.164.227/publicaciones/docs/apuntes_matematicas/31.%20Aplicaciones%20de%20la%20Integral.pdf#)\n",
        "- [La regla de Simpson: la fórmula y cómo funciona](https://www.freecodecamp.org/espanol/news/la-regla-de-simpson-la-formula-y-como-funciona/)\n",
        "- [Regla de Simpson](https://es.wikipedia.org/wiki/Regla_de_Simpson)\n",
        "- [Métodos Numéricos con Python - Parte 1 Cálculo Numérico](https://joanby.github.io/curso-numerico-1/)\n",
        "- [Derivación numérica Python](https://www.youtube.com/watch?v=ZhiuH9l_tB0)\n",
        "- [Derivación e Integración numérica](\n",
        "http://hyperphysics.phy-astr.gsu.edu/hbasees/Math/derint.html#:~:text=La%20derivada%20nos%20puede%20dar,como%20una%20funci%C3%B3n%20de%20x.\n",
        ")"
      ]
    }
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