Simpson 1÷3 múltiple n = 4

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   "source": [
    "# Simpson 1/3 múltiple n = 4\n",
    "\n",
    "###### Se recomienta utilizar el limite de 0 a 3. Implementnado 4 segmentos\n",
    "\n",
    "* Ecuación: \n",
    "$\\int_{}^{}x^2e^x dx$"
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     "text": [
      "Ingrese limite inferior: 0\n",
      "Ingrese limite superior: 3\n",
      "Ingrese numero de segmentos: 4\n",
      "\n",
      "Valor numerico:  99.45683346221226 \n",
      "Valor analítico: 98.42768461593835\n",
      "             Et: 0.010455887998276278 %\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "def f(x):\n",
    "    return (x**2)*(math.exp(x))\n",
    "\n",
    "def S13M(a, b, n):\n",
    "    vn = 0\n",
    "    h = (b-a)/n\n",
    "    for i in range(1,n-1,2):\n",
    "        x = a + i*h\n",
    "        vn = vn + 4*f(x) + (2*f(x+h))\n",
    "    vn = vn + 4*f(b-h) + f(b)\n",
    "    vn = h*vn/3\n",
    "    return vn\n",
    "\n",
    "def va(n):\n",
    "    return (n**2)*(math.exp(n)) - (2*(((math.exp(n))*n) - math.exp(n)))\n",
    "\n",
    "a = float(input(\"Ingrese limite inferior: \"))\n",
    "b = float(input(\"Ingrese limite superior: \"))\n",
    "n = int(input(\"Ingrese numero de segmentos: \"))\n",
    "\n",
    "vn = S13M(a, b, n)\n",
    "va = va(b) - va(a)\n",
    "et = abs((va-vn)/va)\n",
    "\n",
    "print(f\"\"\"\n",
    "Valor numerico:  {vn} \n",
    "Valor analítico: {va}\n",
    "             Et: {et} %\"\"\")"
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