{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fcdc8220-ff32-44a6-a1aa-008c9d2ab047",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f6807c1d-c008-4661-a888-5244338ff765",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x**-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b1095809-d35b-475a-887e-728695022470",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def integrNC(fct, a, b, N, m, n, r, coeff, tol=1e10):\n",
    "    h = (b-a)/m/N\n",
    "    I = 0\n",
    "    for k in range(N):\n",
    "        # Ajout d'un shéma élementaire\n",
    "        Ie = 0\n",
    "        \n",
    "        Xk = a + h*k*m\n",
    "        for i in range(n+1):\n",
    "            Ie += coeff[i] * fct(Xk + (i+r)*h)\n",
    "   \n",
    "        I += Ie * h\n",
    "    \n",
    "    return I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "36508cd9-143a-4174-bc98-6c01634f1fcd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.998686802598624\n"
     ]
    }
   ],
   "source": [
    "I = 0\n",
    "a, b = 1, 5\n",
    "N=100\n",
    "m=1\n",
    "n=1\n",
    "r=0\n",
    "coeff = [.5, .5]\n",
    " \n",
    "while True:\n",
    "    Ie = integrNC(f, a, b, N, m, n, r, coeff)\n",
    "    \n",
    "    \n",
    "    d= b-a\n",
    "    b += d\n",
    "    a += d\n",
    "    # print(I, abs(Ie), abs(Ie)<1e-10)\n",
    "    if abs(I+Ie) - abs(I) < 1e-5:\n",
    "        break\n",
    "    I += Ie\n",
    " \n",
    "print(I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d52567ea-6629-4433-9df9-e3f93de1c36c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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