integracion numerica.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integración numerica\n",
    "\n",
    "\n",
    "$$ f(x) = x^2 $$\n",
    "\n",
    "$$ I =  \\int_0^2 {x^2} dx  = \\left[\\frac{1}{3} x^3\\right]^2_0 = \\frac{2^3}{3} = \\frac{8}{3} = 2.\\bar6$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,4,100)\n",
    "plt.plot(x,x**2)\n",
    "plt.plot\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 0\n",
    "b = 2\n",
    "l = b+a\n",
    "lm = l/2\n",
    "I = l*f(lm)\n",
    "I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sumatoria(f, a, b, N=1):\n",
    "    longitud = b - a \n",
    "    intervalo = longitud / N\n",
    "    print(\"N=%i, lon=%f, long_tot=%f\"%(N,intervalo,longitud))\n",
    "    i = 0\n",
    "    acum = 0\n",
    "    while i < N:\n",
    "        lm = i*intervalo + (intervalo/2)\n",
    "        I = (f(lm))*intervalo\n",
    "        acum = acum + I\n",
    "        i += 1 \n",
    "    return acum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ef62863d50e54072ba3d85647cc0633e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=25, description='intervalos', max=50, min=1), Output()), _dom_classes=('…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(intervalos=(1,50,1))\n",
    "def plot(intervalos):\n",
    "    r = sumatoria(f,0,2, N=intervalos)\n",
    "    print(\"el area es %f\"%r)\n",
    "    x = np.linspace(0,2,100)  #la x de la linea azul\n",
    "    y = np.linspace(0,2, intervalos+1) # x de los puntos naranjas\n",
    "    plt.plot(x,f(x)) # la linea azul\n",
    "    plt.plot(y,f(y), \"o\")#los puntos naranjas\n",
    "    plt.grid()\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.66666667, 1.33333333, 2.        ])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}