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   "source": [
    "#### Regla del trapecio para la integral $$\\int_{1}^{2}\\left ( \\frac{x+2}{x} \\right )^{2}$$"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
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   "source": [
    "import math\n",
    " \n",
    "print(\"=======================================================================\")\n",
    "print(\"Calculo numérico de la regla del trapecio múltiple\")\n",
    "print(\"=======================================================================\")\n",
    "\n",
    "\n",
    "\n",
    "n=int(input(\"número de segmentos = \"))\n",
    "a=float(input(\"valor del límite inferior = \"))\n",
    "b=float(input(\"valor del límite superior = \"))\n",
    "\n",
    "print(\"-----------------------------------------------------------------------------------------------\")\n",
    "print(\"{0:>10s}{1:>20s}{2:>20s}\".format(\"n\", \"integral\", \"et\"))\n",
    "print(\"-----------------------------------------------------------------------------------------------\")\n",
    "\n",
    "vv=5.7725887272\n",
    "fa = ((a+2)/a)**2\n",
    "fb = ((b+2)/b)**2\n",
    "h = (b-a)/n\n",
    "\n",
    "for k in range (n) :\n",
    "    sum=fa\n",
    "    h = (b-a)/(k+1)\n",
    "    for i in range (1,k+1) :\n",
    "        xi = a+(i*h)\n",
    "        fxi = ((xi+2)/xi)**2\n",
    "        sum = sum+(2*fxi)\n",
    "        \n",
    "    sum = sum + fb\n",
    "    sum = h*(sum/2)\n",
    "    I = h*(sum/2)\n",
    "    et=abs((vv-sum)/vv)*100\n",
    "    print(\"{0:10d}{1:20.9f}{2:20.9f}\".format(k+1, sum , et))\n",
    "\n",
    "    \n",
    "print(\"======================================================================\")"
   ]
  }
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