TP_Integration.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "TP_Integration.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMJuUabpM8YbpruY9PbOqUS",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/othoni-hub/ECG1/blob/main/TP_Integration.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TcnuHU_isZj9"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7KqEqysZsjLW"
      },
      "source": [
        "# **CPGE-ECG1** \n",
        "<img src=\"https://drive.google.com/uc?id=12Wo3LubGGT4qOvYFAuLP4CyCuwjKNVuk\" width=\"230\" height=\"150\" align = \"right\"/>\n",
        "\n",
        "## **Ch15 - Notebook : TP - Intégration et calculs approchés d'aires**\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "**O.Thöni - Lycée Saint-Charles Sainte Croix - LE MANS**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WOulo1VC_REm"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from math import sqrt, log, exp\n",
        "\n",
        "def centrax() :\n",
        "    '''paramétrage esthétique des axes dans la représentation graphique d'une fonction'''\n",
        "    ax = plt.gca()\n",
        "    ax.spines['left'].set_position('zero')\n",
        "    ax.spines['right'].set_color('none')\n",
        "    ax.spines['bottom'].set_position('zero')\n",
        "    ax.spines['top'].set_color('none')\n",
        "    "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F7wewfpq_RHR"
      },
      "source": [
        "On cherche une valeur approchée de l'aire sous la courbe de la fonction d'expression $f(x) = x^3 + x^2 + 6x + 5$, entre -3 et 3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p0Inah71_RHV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "3cbe0b9c-7525-4b6a-de01-ebbb184c4697"
      },
      "source": [
        "a = -3\n",
        "b = 3\n",
        "\n",
        "# Définition de la fonction\n",
        "def f(x):\n",
        "    y = x**3 + x**2 -6*x + 5\n",
        "    return y\n",
        "titre = ('$f(x) = x^3 + x^2 - 6x + 5$')\n",
        "\n",
        "# Représentation graphique\n",
        "def graph(f):\n",
        "    xx = np.arange(a,b+0.1,0.1) # liste numpy de a à b avec un pas de 0.1 (les listes natives avec range sont des listes d'entiers)\n",
        "    yy = []\n",
        "\n",
        "    for x in xx :\n",
        "        yy.append(f(x))\n",
        "    \n",
        "    p1 = plt.plot(xx,yy,'r',linewidth=1)\n",
        "\n",
        "    centrax()\n",
        "\n",
        "    plt.xlim(a-0.5,b+0.5)\n",
        "    plt.title(titre)\n",
        "    \n",
        "graph(f)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p7r8MC-x_RIA"
      },
      "source": [
        "### 1. méthode des rectangles\n",
        "\n",
        "**<span style=\"color: #D17460\">TSpé - TCompl </span>**\n",
        "\n",
        "**<span style=\"color: #26B260\">Python : listes par compréhension</span>**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NAmkHq0M_RIE"
      },
      "source": [
        "titre = ('$f(x) = x^3 + x^2 - 6x + 5$')\n",
        "def rectangles(n):\n",
        "    pas = (b-a)/n\n",
        "    Aire = 0\n",
        "\n",
        "    x = [a + k*pas for k in range(n)] # liste définie par compréhension\n",
        "    Rectangles = [pas*f(x[k]) for k in range(n)]\n",
        "    S = sum(Rectangles) #somme des termes de la liste 'Rectangles'\n",
        "    return S\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RZY-p6t8_RIS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2be59645-cd46-4bce-f0ed-c9c441cc751b"
      },
      "source": [
        "rectangles((b-a)*5) #unité divisée en 5"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "46.24000000000001"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xO6vAjrl_RIf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6ced41a4-6c29-4b93-9c09-2279a897881d"
      },
      "source": [
        "rectangles((b-a)*100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "47.910100000000035"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UnqCs5O2_RIz",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dbf319fe-5254-4067-d19d-491f7369b97b"
      },
      "source": [
        "rectangles((b-a)*100000) "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "47.999910000102716"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "stmQKhZC_RJD"
      },
      "source": [
        "**_illustration graphique pour l'unité subdivisée en 2_**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ggmXeYGt_RJH",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "b5a5ef6e-38fd-40d9-fc53-0957bdb4aaf6"
      },
      "source": [
        "graph(f)\n",
        "\n",
        "n = (b-a)*2\n",
        "pas = (b-a)/n\n",
        "x = [a + k*pas for k in range(n)]\n",
        "\n",
        "for k in range(n-1) :\n",
        "    plt.plot([x[k],x[k]],[0,f(x[k])], 'b',linewidth = 1 )\n",
        "    if f(x[k]) > f(x[k+1]) :\n",
        "        plt.plot([x[k+1],x[k+1]],[0,f(x[k])], 'b',linewidth = 1 )\n",
        "    plt.plot([x[k],x[k+1]],[f(x[k]),f(x[k])], 'b',linewidth = 1)\n",
        "    \n",
        "plt.plot([x[-1],x[-1]],[0,f(x[-1])], 'b',linewidth = 1 ) \n",
        "plt.plot([x[-1],b],[f(x[-1]),f(x[-1])], 'b',linewidth = 1 )\n",
        "plt.plot([b,b],[0,f(b)], 'b',linewidth = 1 )  \n",
        "\n",
        "plt.show()\n",
        "\n",
        "print('Aire estimée : ', rectangles(n))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Aire estimée :  43.75\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W8W3CECH_RJT"
      },
      "source": [
        "### 2. méthode des trapèzes\n",
        "\n",
        "**<span style=\"color: #D17460\">TSpé </span>**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vzrzcPmC_RJZ"
      },
      "source": [
        "def trapezes(n):\n",
        "    pas = (b-a)/n\n",
        "    Aire = 0\n",
        "\n",
        "    x = [a + k*pas for k in range(n+1)] # liste définie par compréhension\n",
        "    Trapezes = [pas*(f(x[k])+f(x[k+1]))/2 for k in range(n)]\n",
        "    S = sum(Trapezes) \n",
        "    return S"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dvRjOKHD_RJr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8ae0ca61-9ddd-49f3-b64f-dbb25b78b141"
      },
      "source": [
        "trapezes((b-a)*5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "48.040000000000006"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bpcr7wb0_RJ3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "95523614-d1c4-484c-80e3-d0702479a210"
      },
      "source": [
        "trapezes((b-a)*100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "48.0001"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UugwfwyQ_RKG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f5a08c55-3f3b-45e7-9d39-610f408cc849"
      },
      "source": [
        "trapezes((b-a)*100000)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "48.00000000009952"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zxp4O2-X_RKP"
      },
      "source": [
        "**_illustration graphique pour l'unité subdivisée en 2_**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yHZLvZRX_RKR",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "5eb13eca-9b07-49dc-83d1-e2774562de3a"
      },
      "source": [
        "graph(f)\n",
        "\n",
        "n = (b-a)*2\n",
        "pas = (b-a)/n\n",
        "x = [a + k*pas for k in range(n+1)]\n",
        "\n",
        "for k in range(n) :\n",
        "    plt.plot([x[k],x[k]],[0,f(x[k])], 'b',linewidth = 1 )\n",
        "    plt.plot([x[k],x[k+1]],[f(x[k]),f(x[k+1])], 'b',linewidth = 1)\n",
        "    \n",
        "#plt.plot([x[-1],x[-1]],[0,f(x[-1])], 'b',linewidth = 1 ) \n",
        "#plt.plot([x[-1],b],[f(x[-1]),f(x[-1])], 'b',linewidth = 1 )\n",
        "plt.plot([b,b],[0,f(b)], 'b',linewidth = 1 )  \n",
        "\n",
        "plt.show()\n",
        "\n",
        "print('Aire estimée : ', trapezes(n))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Aire estimée :  48.25\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rbysxINd_RKc"
      },
      "source": [
        "### 3. méthode des milieux\n",
        "\n",
        "**<span style=\"color: #D17460\">TSpé </span>**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Stdh68m2_RKf"
      },
      "source": [
        "def milieux(n):\n",
        "    pas = (b-a)/n\n",
        "    Aire = 0\n",
        "\n",
        "    x = [a + k*pas for k in range(n+1)] # liste définie par compréhension\n",
        "    RectanglesMilieux = [pas*f((x[k]+x[k+1])/2) for k in range(n)]\n",
        "    S = sum(RectanglesMilieux) \n",
        "    return S"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ioynG1GM_RKz",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c3c506d2-6f88-4e4e-995c-72cba6fd89e1"
      },
      "source": [
        "milieux((b-a)*5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "47.98000000000002"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uw34cCFI_RK9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6ae78180-18bc-4558-e1f0-e8c06d698b00"
      },
      "source": [
        "milieux((b-a)*100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "47.99994999999999"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ko7JR4dm_RLG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9bc12275-670f-48a5-926f-c0e54c009c81"
      },
      "source": [
        "milieux((b-a)*100000)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "47.99999999995055"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tD9INnoz_RLQ"
      },
      "source": [
        "**_illustration graphique pour l'unité subdivisée en 2_**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j3KjEJ0b_RLS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "10e82bdd-7a20-40cc-b033-310a78aad1d1"
      },
      "source": [
        "graph(f)\n",
        "\n",
        "n = (b-a)*2\n",
        "pas = (b-a)/n\n",
        "x = [a + k*pas for k in range(n+1)]\n",
        "\n",
        "for k in range(n) :\n",
        "    plt.plot([x[k],x[k]],[0,f((x[k]+x[k+1])/2)], 'b',linewidth = 1 )\n",
        "    plt.plot([x[k],x[k+1]],[f((x[k]+x[k+1])/2),f((x[k]+x[k+1])/2)], 'b',linewidth = 1)\n",
        "    \n",
        "#plt.plot([x[-1],x[-1]],[0,f(x[-1])], 'b',linewidth = 1 ) \n",
        "#plt.plot([x[-1],b],[f(x[-1]),f(x[-1])], 'b',linewidth = 1 )\n",
        "plt.plot([b,b],[0,f(b)], 'b',linewidth = 1 )  \n",
        "\n",
        "plt.show()\n",
        "\n",
        "print('Aire estimée : ', milieux(n))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Aire estimée :  47.875\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M1KJeWvN_RLg"
      },
      "source": [
        "### 4. Une méthode utilisant l'aléatoire : la méthode de Monte-Carlo\n",
        "\n",
        "**<span style=\"color: #D17460\">TSpé - TCompl </span>**\n",
        "\n",
        "**<span style=\"color: #26B260\">Python : aléatoire avec le module random, passage d'une fonction en parmamètre d'une fonction !!!</span>**\n",
        "\n",
        "On encadre la courbe par un rectangle (ici : abscisses entre -3 et 3, ordonnées entre 0 et la valeur maximale de f sur l'intervalle).\n",
        "\n",
        "On tire des \"fléchettes aléatoires\" dans ce rectangle, la proportion d'entre elles tombant en-dessous de la courbe donne une valeur approchée de la proportion de l'aire cherchée par rapport à celle du rectangle."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bQLq4hzN_RLj"
      },
      "source": [
        "from random import uniform\n",
        "\n",
        "# recherche du maximum de f sur [a;b]\n",
        "x_du_max = a\n",
        "xx = np.arange(a,b+0.1,0.1)\n",
        "\n",
        "for x in xx:\n",
        "    if f(x)>f(x_du_max):\n",
        "        x_du_max = x\n",
        "y_max = f(x_du_max)\n",
        "\n",
        "# définition de la fonction MonteCarlo et représenttion de la simulation\n",
        "def monte_carlo(f,N):\n",
        "    graph(f)\n",
        "    sous_la_courbe = 0\n",
        "    for k in range(N+1):\n",
        "        x_point = uniform(a,b) # effectue un tirage aléatoire selon la loi uniforme continue sur [a;b]\n",
        "        y_point = uniform(0,y_max)\n",
        "        if y_point < f(x_point):\n",
        "            sous_la_courbe = sous_la_courbe + 1\n",
        "            plt.plot(x_point,y_point,'g',marker = '+') # croix verte\n",
        "        else :\n",
        "            plt.plot(x_point,y_point,'r',marker = '+') # croix rouge\n",
        "       \n",
        "    plt.show()\n",
        "    return sous_la_courbe / N\n",
        "    \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DObpOXUL_RL2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "87c7bd33-6261-4dcf-8ed8-cceb1374c8ac"
      },
      "source": [
        "prop = monte_carlo(f,100)\n",
        "\n",
        "print('Aire estimée : ', prop * (b-a)*y_max)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Aire estimée :  52.44000000000034\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "seO3YMOR_RL_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "33279884-1c47-4833-a5f8-50bd6e700e88"
      },
      "source": [
        "prop = monte_carlo(f,1000)\n",
        "\n",
        "print('Aire estimée : ', prop * (b-a)*y_max)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Aire estimée :  45.678000000000296\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HYlU3UtY_RML"
      },
      "source": [
        "**_Exercice_**\n",
        "\n",
        "Adapter les méthodes ci-dessus au calcul de $\\int_{-1}^{1} \\sqrt{1-x^2} dx$ pour obtenir des valeurs approchées de $\\pi$\n",
        "\n",
        "**<span style=\"color: #D17460\">1Spé : aire sous la courbe, estimation de $\\pi$ par la méthode de Monte Carlo </span>**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "flVM9I8Y_RMO"
      },
      "source": [
        "**_Remarque_**\n",
        "\n",
        "**<span style=\"color: #26B260\">Python : lambda-fonction</span>**\n",
        "\n",
        "Comme on peut passer la fonction intégrée en paramètre, on peut faire usage d'une lamba-fonction :\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1BKdxJ32_RMR",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        },
        "outputId": "9c36bf77-0a5e-4ab8-d1d3-008410d6e2c5"
      },
      "source": [
        "a = -1\n",
        "b = 1\n",
        "titre = 'y = $\\sqrt{1-x^2}$'\n",
        "g = lambda x: sqrt(1-x*x)\n",
        "plt.axis('equal') # repère orthonormé\n",
        "\n",
        "# recherche du maximum de f sur [a;b]\n",
        "x_du_max = a\n",
        "xx = np.arange(a,b+0.1,0.1)\n",
        "\n",
        "for x in xx:\n",
        "    if g(x)>g(x_du_max):\n",
        "        x_du_max = x\n",
        "y_max = g(x_du_max)\n",
        "\n",
        "prop = monte_carlo(lambda x: sqrt(1-x*x), 1000)\n",
        "\n",
        "print('Aire estimée : ', 2*prop * 2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Aire estimée :  3.216\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cpEYCc9o41Ue"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}