{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "![En tête general](img/En_tete_general.png)\n", "\n", "\n", "*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n", "\n", " Pour exécuter une saisie Python, sélectionner la cellule et valider avec SHIFT+Entrée.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Approximation d’une intégrale par la méthode des rectangles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Certaines fonctions n’ont pas de primitives qui peuvent s’écrire à l’aide des fonctions usuelles.* \n", "\n", "*C’est par exemple le cas de la fonction $f$ définie sur $\\mathbb{R}$ par $f(x)=e^{-x^2}$.* \n", "\n", "*Le but de cette activité est d’obtenir malgré tout des valeurs approchées de l’intégrale\n", "$K=\\int_{0}^{1}{e^{-x²}dx}$*. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## I. Introduction de la méthode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1. Placer les points $M_0$ ; $M_1$ ; $M_2$ ; $M_3$ et $M_4$ de la courbe de $f$ d’abscisses respectives $0$ ; $\\displaystyle \\frac{1}{4}$ ; $\\displaystyle \\frac{2}{4}$; $\\displaystyle \\frac{3}{4}$ et $\\displaystyle \\frac{4}{4}$.__\n", "\n", "![Rectangles à compléter](img/Methode_rectangles_intro.png)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__2. A l’aide de ces points, inscrire $4$ rectangles sous la courbe de $f$, de largeur $\\displaystyle \\frac{1}{4}$ et de longueur maximale.__\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__3. Ecrire une fonction Python f qui prend x en argument et renvoie l’image de $x$ par $f$.__\n", "\n", "*Important : Ne pas utiliser la fonction exp. Utiliser les notations de puissances à partir de la constante e, obtenue avec from math import e.* \n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from math import e\n", "# Ecrire la fonction\n", "\n", "def f(x):\n", " return e**(-x**2)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.36787944117144233" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Tester la fonction\n", "f(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Ecrire une fonction Python Aire_rect qui reçoit en argument la largeur l et la longueur L d’un rectangle et renvoie son aire.__\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Ecrire la fonction\n", "def Aire_rect(l,L):\n", " return l*L" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Tester la fonction\n", "Aire_rect(3,5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__A l’aide de ces fonctions, calculer la somme des aires des $4$ rectangles précédents, et en déduire un minorant de $K$.__" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6639690279468116" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Effectuer les saisies nécessaires\n", "Aire_rect(1/4,f(1/4))+Aire_rect(1/4,f(2/4))+Aire_rect(1/4,f(3/4))+Aire_rect(1/4,f(4/4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## II. Automatisation de la construction et du calcul " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1. La fonction ci-dessous trace la courbe représentative de $f$ sur l’intervalle $[0;1]$ et construit les 4 rectangles sous la courbe de $f$. \n", "Tester cette fonction.__" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib.patches as ptc\n", "import numpy as np\n", "\n", "def Methode_rectangle(n=4):\n", " \n", " # tracé de la courbe de f\n", " prec=0.05\n", " abs_fonc = np.arange(0,1+prec,prec)\n", " ord_fonc = f(abs_fonc)\n", " plt.plot(abs_fonc,ord_fonc,color='green')\n", " \n", " ax = plt.gca()\n", " \n", " #initialisation du compteur\n", " Aire_inf=0\n", " \n", " # tracé des rectangles et calcul de l'aire\n", " l=1/n\n", " for k in range(n):\n", " x=k*1/n\n", " L=f(x+1/n)\n", " #Rectangle défini par le point en bas à gauche,\n", " #sa largeur l et sa longueur L\n", " rect=ptc.Rectangle( (x,0) , l, L, fill=False)\n", " ax.add_patch(rect) \n", " \n", " #incrément du compteur\n", " Aire_inf = Aire_inf + Aire_rect(l,L)\n", "\n", " # affichage de l'aire sous la figure\n", " plt.text(0,-0.2,'Aire='+str(Aire_inf)) \n", " # reglage des bornes des axes du repere\n", " plt.axis([0,1,0,1]) \n", " # affichage \n", " plt.show() \n", "\n", " # (Ces fonctionnalités sont désactivées dans la version Notebook)\n", " # attente d'une action de clic sur la fenetre puis fermeture\n", " # plt.waitforbuttonpress() \n", " # plt.close()\n", "\n", " return Aire_inf\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "0.6639690279468116" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Test de la fonction\n", "Methode_rectangle()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__2. Prévoir les valeurs successives prises par les variables x, l et L dans la boucle en complétant ce tableau :__\n", "\n", "\n", "| $k$ | 0 | 1 | 2 | 3 |\n", "| :-------: |:--: | :--: | :--: | :--: |\n", "| $x$ | | | | |\n", "| $l$ | | | | |\n", "| $L$ | | | | |\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Compléter la fonction précédente pour qu’elle renvoie Aire_inf qui est la somme des aires de ces rectangles.__\n", "\n", "\n", "*Aides :*\n", "*On pourra ajouter un compteur qui s’incrémente à chaque étape de la boucle, en utilisant la fonction* Aire_rect *précédemment écrite.* \n", "*On pourra éventuellement utiliser l’instruction* plt.text(0,-0.2,’Aire=’+str(Aire_inf)) *pour afficher cette aire sur le graphique.* \n", "\n", "__Tester et vérifier qu’on retrouve le résultat de la question I.3.__" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "0.6639690279468116" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Tester la fonction modifiée\n", "Methode_rectangle()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__3. Modifier la fonction pour qu’elle reçoive en argument le nombre n de rectangles souhaités, et adapter l’affichage et le calcul. Tester pour $n=10$ puis pour $n=100$.__\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "(0.7146047681903215, 0.7436573986738273)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Effectuer les tests\n", "Methode_rectangle(10) , Methode_rectangle(100) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## III. Recherche de la précision de la méthode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1. A l'aide de la figure dynamique ci-dessous, vérifier les résultats des questions I.3 et II.3.__\n", "\n", "*(Pour faire apparaître et activer la figure dynamique, sélectionner la cellule et valider avec SHIFT+Entrée).*\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\t\n", "\t\n", "\t\n", "\t\t
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On considère de la même façon la somme $S_n$ des aires de $n$ rectangles de même largeur construits au-dessus de la courbe de $f$ sur l’intervalle $[0;1]$ (utiliser le curseur vert sur la figure dynamique fournie)__\n", "\n", "__Donner une expression de $S_n$ similaire à celle de $s_n$.__\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__4. Exprimer $S_n-s_n$ en fonction de $n$.__\n", "\n", "__En admettant que $\\displaystyle s_n \\leqslant \\int_{0}^{1} \\ e^{-x²} dx \\ \\leqslant S_n $, en déduire que :\n", "$\\displaystyle 0 \\leqslant ∫_0^1 \\ e^{-x^2} dx \\ -s_n \\leqslant \\frac{1}{n} $ .__\n", "\n", "__Quelle valeur de $n$ faut-il choisir pour que $s_n$ soit une valeur approchée de $K$ à $10^{-4}$ près ?__\n", "\n", "__Donner une valeur approchée à $10^{-4}$ près de cette intégrale $K$ à l’aide de vos fonctions Python de la partie II.__\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ka+xOA9rC0YOOZvX01fTr1C/eupoxDemISGarvMbuRCBXUzHXhwJfRJqHalMxrz58NWeXnk2r/Fbx1tWMKPBFpHnpAswABgCfwK0n3crxQ4/XVMxpUOCLSPPUi3BEz4Ew4oARXDHzCqb1nhZzUZlNgS8izZcBhxCmYu4Ah/U7jMtnXM7BXQ+Ot64MpcAXkeYvjzAZ+2SgAE4dfSo/LPshhW0LYy4ssyjwRSR7tAKmACXATrjo0Is4d/y5tCloE3NhmUGBLyLZpyNhx+7BwGdw/bHXs3jEYvJz82MuLF4KfBHJXsWEC6z2hJxtOfzy9F9y1MCjEjtVg6ZWEJHsVQHcDNwJu3bu4pi7j2H8mvG6uHodqIcvIs1HDmGqhjKgHRzR/whWz1jN4C6DYy2rKWlIR0SSJZ9wmaWJQAEsHrWYH5b9kKJ21S+3nX0U+CKSTPsBkwiHc+6Cf536r1ww4QLat2wfc2GNR4EvIsnWgTAj51Dgc7jyyCs5o+SMrLz4igJfRASgkHAoZx/gY7h90e0sGLIgq+boUeCLiKQ6iHAoZ2GYo+eyGZdxaJ9D466qQSjwRUSqq5yjZxrQEab3ns6l0y+lpKgk5sLqR4EvIrInuYRpGiYBrcNVty6ZegmDugyKubC6UeCLiNSmgHDVrfFAPpw88mQunnIxPTv0jLmwfaPAFxFJ136E4/fHhIfLJizjwkkX0rV11zirSpsCX0RkX7UjnLE7HPgafnDoD/j+uO9n/DH8CnwRkbrqRNixezDwOVwx5wrOKDkjY6+zq8AXEamvQsJVt/oCn8J/H//fnDz8ZPJy8mIubHcKfBGRhtKLEPzdIe+TPH6x+BfMHTw3Y07eUuCLiDS0AYShnm7h5K3/mP4flPcpj30efgW+iEhjMGAIMBXoCBN7TGTV1FWU9SqLryQFvohII8oFRhJO3moH03pPY2XZSib0mNDkpSjwRUSaQh4wihD8baC8Tzkrp65kTNGYJitBgS8i0pTyCdM1TABaw3f6f4eVZSsZUTii0d9agS8iEocCwpW3xgOtwjw9F0+5mCHdhjTaWyrwRUTi1IIwT8/YcP/YQ47l4rKLGdh5YIO/lQJfRCQTtKIq+PPgxOEnsmLKCvru37fB3qI+gZ/WmQRmNsvMXjezrWa2fC/tSsxsp5nNrUsxIiLN2hfA48BVwNNw28bb6Hd1Pxb/ajFvffxWrKVBGj18M8sF3iBcP6YCWA8scPdXamj3GPAlsMbd76llverhi0h2a0OYmXM0YHDamNNYPnE5vTr0qvMqG7uHPwbY6u5vuvtXwFpgTg3tzgLuBd6vSyEiIlnnM+AR4Brgefjpcz+l95W9WfyrxWzdtrXJy0kn8IuAd1IeV0TPfcPMioCjgBv2tiIzW2JmG8xsw74WKiLSbH0K/Bq4GtgAazasod/V/Vh430Je++C1JisjncCvaeKI6sMxVwEXuPvOva3I3W9099F1/TkiItKsfQo8TEjMZ+C2Dbcx6NpBzL9nPlve39Lob59O4FcA3VMeFwPvVmszGlhrZm8Bc4HrzOzIhihQRCTrfAb8lhD8f4K7nr+LIdcP4Zi7j+GF915otLdNZ6dtHmGn7XTg/xJ22h7n7i/vof0twEPaaSsikqZWhEM5S4GW4czdH0z+QY1TNjTqTlt33wEsBR4FXgXudveXzex0Mzu9Lm8qIiIpvgB+T+jxPw4PbXqI0ptKmXX7LP789p8b7G104pWISKYpIMzVMx5oDVN7TWXFlBVM6TmFnJwcnWkrIpJ18gmzc04A2ob5+P90yp8U+CIiWSuPMB//BODH1DnwM+vqvCIi8m07gOeAjfVbTWZclVdERGq31zOdaqfAFxFJCAW+iEhCKPBFRBJCgS8ikhAKfBGRhFDgi4gkhAJfRCQhFPgiIgmhwBcRSQgFvohIQijwRUQSQoEvIpIQCnwRkYRQ4IuIJIQCX0QkIRT4IiIJocAXEUkIBb6ISEIo8EVEEkKBLyKSEAp8EZGEUOCLiCSEAl9EJCEU+CIiCaHAFxFJCAW+iEhCKPBFRBJCgS8ikhAKfBGRhFDgi4gkRFqBb2azzOx1M9tqZstreP14M9sc3Z4ys2ENX6qIiNRHrYFvZrnAT4DZwGBggZkNrtbsr8AUdx8KrAJubOhCRUSkftLp4Y8Btrr7m+7+FbAWmJPawN2fcvePoofPAMUNW6aIiNRXOoFfBLyT8rgiem5PFgMP16coERFpeHlptLEanvMaG5pNJQT+xD28vgRYknZ1IiLSYNIJ/Aqge8rjYuDd6o3MbChwEzDb3T+saUXufiPR+L6Z1filISIijSOdIZ31QD8z621mBcB84IHUBmbWA1gHnOjubzR8mSIiUl+19vDdfYeZLQUeBXKBNe7+spmdHr1+A7AC6ARcZ2YAO9x9dOOVLSIi+8rc4xlZ0ZCOiEidbKxrh1pn2oqIJIQCX0QkIRT4IiIJocAXEUkIBb6ISEIo8EVEEkKBLyKSEAp8EZGEUOCLiCSEAl9EJCEU+CIiCaHAFxFJCAW+iEhCKPBFRBJCgS8ikhAKfBGRhFDgi4gkhAJfRCQhFPgiIgmhwBcRSQgFvohIQijwRUQSQoEvIpIQCnwRkYRQ4IuIJIQCX0QkIRT4IiIJocAXEUkIBb6ISEIo8EVEEkKBLyKSEAp8EZGEUOCLiCSEAl9EJCEU+CIiCZFW4JvZLDN73cy2mtnyGl43M7smen2zmY1s+FJFRKQ+ag18M8sFfgLMBgYDC8xscLVms4F+0W0JcH0D1ykiIvWUTg9/DLDV3d9096+AtcCcam3mALd68AzQwcwKG7hWERGph7w02hQB76Q8rgBK02hTBLyX2sjMlhB+AQBsB7bsS7FZrDPwQdxFZAhtiyraFlW0LaoMqOuC6QS+1fCc16EN7n4jcCOAmW1w99FpvH/W07aoom1RRduiirZFFTPbUNdl0xnSqQC6pzwuBt6tQxsREYlROoG/HuhnZr3NrACYDzxQrc0DwMLoaJ2xwCfu/l71FYmISHxqHdJx9x1mthR4FMgF1rj7y2Z2evT6DcBvgMOArcDnwKI03vvGOledfbQtqmhbVNG2qKJtUaXO28LcvzXULiIiWUhn2oqIJIQCX0QkIRo98DUtQ5U0tsXx0TbYbGZPmdmwOOpsCrVti5R2JWa208zmNmV9TSmdbWFmZWb2opm9bGZ/bOoam0oa/0fam9mDZrYp2hbp7C9sdsxsjZm9b2Y1nqtU59x090a7EXby/gU4CCgANgGDq7U5DHiYcCz/WODZxqwprlua22I80DG6PzvJ2yKl3eOEgwLmxl13jP8uOgCvAD2ix13jrjvGbXEhcFl0vwuwDSiIu/ZG2BaTgZHAlj28XqfcbOwevqZlqFLrtnD3p9z9o+jhM4TzGbJROv8uAM4C7gXeb8rimlg62+I4YJ27vw3g7tm6PdLZFg60NTMD2hACf0fTltn43P0JwmfbkzrlZmMH/p6mXNjXNtlgXz/nYsI3eDaqdVuYWRFwFHBDE9YVh3T+XfQHOprZH8xso5ktbLLqmlY62+JaYBDhxM6XgGXuvqtpyssodcrNdKZWqI8Gm5YhC6T9Oc1sKiHwJzZqRfFJZ1tcBVzg7jtDZy5rpbMt8oBRwHSgFfC0mT3j7m80dnFNLJ1tUQ68CEwD+gCPmdmT7v5pI9eWaeqUm40d+JqWoUpan9PMhgI3AbPd/cMmqq2ppbMtRgNro7DvDBxmZjvc/f4mqbDppPt/5AN3/yfwTzN7AhgGZFvgp7MtFgGrPQxkbzWzvwIDgeeapsSMUafcbOwhHU3LUKXWbWFmPYB1wIlZ2HtLVeu2cPfe7t7L3XsB9wBnZGHYQ3r/R34FTDKzPDPbjzBb7atNXGdTSGdbvE34pYOZdSPMHPlmk1aZGeqUm43aw/fGm5ah2UlzW6wAOgHXRT3bHZ6FMwSmuS0SIZ1t4e6vmtkjwGZgF3CTu2fd1OJp/rtYBdxiZi8RhjUucPesmzbZzO4EyoDOZlYBXATkQ/1yU1MriIgkhM60FRFJCAW+iEhCKPBFRBJCgS8ikhAKfBGRhFDgi4gkhAJfRCQhFPgiIgmhwBcRSQgFvohIQijwRUQSQoEvIpIQCnwRkYRQ4IuIJIQCX0QkIRT4IiIJocAXEUkIBb6ISEIo8EVEEiL2wDezo8zMzWxg9PhAM7unEd5nlJm9ZGZbzewai64SXq3N8Wb2Ysptl5kNr9bmATPbUu2575nZK2b2spndET03tdq6vjSzI6PXppnZ82a2xcx+bmZ5Ke+/Obo9ZWbDUt7jraj+F81sQ8rz/2lmr0XL3GdmHVJeG2pmT0d1vWRmLaPn/93M3jGzz6p9jh+n1PuGmX2c8tojZvaxmT1UbZmfmdmm6P3vMbM20fNlZvZJyvpWRM93N7Pfm9mrUV3Lqq3vLDN7PXrt8j3/jYrIPnP3WG/A3cCTwMW1tMur5/s8B4wjXOn+YWB2Le2HAG9We+5o4A5gS8pz/YAXgI7R4641rGt/YBuwH+FL9h2gf/TaSmBxdH98ynpmA8+mrOMtoHMN655ZuW2Ay4DLKrcXsBkYFj3uBORG98cChcBne/n8ZwFrUh5PB44AHqrWrl3K/SuB5dH9supto+cLgZHR/bbAG8Dg6PFU4P8ALfa0LXXTTbe632Lt4Ue9wQnAYmB+9Fyvyh60mZ1sZr80sweB35pZazNbY2brzewFM5uT5vsUEoLpaXd34FbgyFoWWwDcWa3W/w1cUq3dqcBP3P0jAHd/v4Z1zQUedvfPCcG73d3fiF57DDgmWvapyvUAzwDFtX02d/+tu++oYZmZwGZ33xS1+9Ddd0b3n3H392pZ9W6f391/B/yjhvf/FCD6xdQK8Frqfc/dn4/u/wN4FSiKXv4XYLW7b49er2lbikgdxT2kcyTwSBR+28xsZA1txgEnufs04N+Ax929hNAb/M/oS2BAteGT1FsHQqBUpKyzgqqQ2ZNjSQk8YBXwI+Dzau36A/3N7M9m9oyZzaphXfNT1vUBkG9mo6PHc4HuNSyzmPBLpJITvvQ2mtmSPdR8Ssoy/QE3s0ej4aPz97DMt5hZT6A38Hia7W8G/gcYCPxXykvjouGeh83s4BqW6wWMAJ5NqXmSmT1rZn80s5J0axaR2uXF/P4LgKui+2ujxz+p1uYxd98W3Z8JfNfMzo0etwR6uPurwPA9vUlN4/XspSdqZqXA5+5e+UtjONDX3c+JQipVHmFYp4zQu37SzA5x94+jZQsJw0OPAri7m9l84Mdm1gL4LbAjdYVmNpUQ+BNTnp7g7u+aWVfgMTN7zd2fSFnm36L1/CKlrolACeFL6ndmtjHqqddmPnBP5S+C2rj7IjPLJYT9scDNwPNAT3f/zMwOA+4nbKfKetsA9wL/q/JXQlRzR8KQUwlwt5kdFP0qE5F6ii3wzawTMA04xMwcyCWE8HXVmv4zdTHgGHd/vdq6BgB37eGtygg9+tThkWLg3b2Ul9ojh/ArY5SZvUXYZl3N7A/uXrnuZ9z9a+CvZvY6IdjWR8t+D7gveh0Ad38amBTVPpPQs638LEOBmwj7GD5MWebd6M/3zew+YAzwRLTMScB3gOkp4VgB/NHdP4ja/AYYCaQb+Gem0e4b7r7TzO4CzgNuTglx3P03ZnadmXV29w/MLJ8Q9r9w93Upq6kA1kWf4Tkz2wV0Bv6+L7WISM3iHNKZC9zq7j3dvZe7dwf+yt7HrR8FzqrssZvZCAB3f93dh+/h9nE0Xv0PMxsbLbsQ+FVNb2BmOcA8wi8OovVf7+4HunsvQq/5jSjsIfRcp0bLdiaE95spq9xtLDxq1zX6swVwAXBD9LgHsA44MWWMn2jYqm3lfcIvncpfH7OidXw32keQuq2Gmtl+Fo4CmgK8spdtW/leAwi97KfTaGtm1rfyPmGn7mvR4wNS/p7GEP6tfRg99zPgVXe/stoq7yd0AjCz/kABYQhMRBpAnIG/ALiv2nP3AhfuZZlVQD6wOdqxu2of3u9fCD3nrcBfiMa6zey7ZrYypd1koMLd3/z2Kmr0KCHIXgF+D5xX2TOPhn+6A3+stsx5ZvYq4SiaB929cqx8BWGn7nW2++GX3YA/mdkmwtFGv3b3R6LXriUc7fJYtMwNANHO3ysJvzReBJ53919HdV1uZhXAfmZWYWYXp9S2AFhbfRjFzJ4EfglMj5YpJ/zi+rmZvQS8RDgCp3JbzgW2RDVfA8yP1jkBOBGYlrKf5bBomTXAQdHf7VrCvhsN54g0ENP/JxGRZIj7KB0REWkiCnwRkYRQ4IuIJIQCX0QkIRT4IiIJocAXEUkIBb6ISEIo8EVEEuL/A+nCPznn0BuCAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "0.7467925261713526" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Effectuer les saisies nécessaires\n", "Methode_rectangle(10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Georg Friedrich Bernhardt Riemann (1826-1866) est à l’origine de cette méthode d’approximation d’intégrales à l’aide de rectangles\n", "\n", "![Riemann](img/Methode_rectangles_Riemann.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n" ] } ], "metadata": { "celltoolbar": "Raw Cell Format", "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": "3.7.10" } }, "nbformat": 4, "nbformat_minor": 2 }