{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 関数の積分\n",
    "\n",
    "今回の授業では一次元の関数の積分を考えます。\n",
    "\n",
    "> ## 復習\n",
    ">\n",
    "> Wikipediaの定積分の定義を引用し、積分の概念を復習します。\n",
    ">\n",
    "> 実数直線上の区間 $[a, b]$ 上で定義される実変数 $x$ の関数 $f$ の定積分 \n",
    "> $$\\int_a^b f(x)~dx$$\n",
    "> は、略式的に言えば $f$ のグラフと $x$軸、および $x = a$ と $x = b$ で囲まれる $xy$平面の領域の符号付面積として定義される。\n",
    "\n",
    "![定積分のイメージ](https://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Integral_example.svg/220px-Integral_example.svg.png)\n",
    "\n",
    "\n",
    "現代的な積分の概念にはリーマン積分、ルベーグ積分などがあります。今回の授業ではリーマン積分の定義を考察します。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 積分の概念\n",
    "\n",
    "初めに、$x=0$ から $x=1$ までの間で $f(x)=\\sqrt{x}+1$ によって与えられる曲線 $y=f(x)$ を考え、\n",
    "「$0$ から $1$ までの区間において $f$ の下にある領域の面積はいくらか」\n",
    "という問いを考えます。この（未知の）面積を $f$ の積分と呼んで\n",
    "\n",
    "$$\\int_{0}^{1}{\\sqrt {x}}+1~ dx $$\n",
    "\n",
    "で書き表します。\n",
    "\n",
    "![積分の例](http://www.ces-alpha.org/download/gs/?label=F7&conf_id=CM2018&verify=01914)\n",
    "\n",
    "> ニュートンとライプニッツが提案した微分積分学の基本定理（１７世紀）によりますと、上記の積分を$f(x)$の原始関数$F(x)=\\frac{2}{3}x^{3/2}+x$を利用することで算出できます。\n",
    ">\n",
    "> $$\\int_{0}^{1}{\\sqrt {x}}+1 ~ dx  = F(1) - F(0) = \\frac{5}{3}$$\n",
    ">\n",
    ">微分積分学の基本定理が発見されるまで、積分は微分とは関係ない「面積」という概念で理解されていました。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 面積の近似計算\n",
    "\n",
    "$f(x)=\\sqrt{x}+1$の$[0,1]$における積分の近似方法を考えます。\n",
    "\n",
    "\n",
    "### 2.1 準備：グラフを描く\n",
    "\n",
    "\n",
    "まず、曲線$y=f(x)$のグラフを描きます。\n",
    "<!--\n",
    "%関数fを定義する\n",
    "function value=f(x)\n",
    "    value = sqrt(x)+1;\n",
    "end\n",
    "\n",
    "% グラフを描くOctaveの関数を定義します。\n",
    "function draw_f()\n",
    "   x=0:0.001:1;\n",
    "   y=f(x);\n",
    "   plot(x,y,'r-');\n",
    "   hold on %現在グラフの上に新しいグラフを描く（重ねて）\n",
    "   grid on  %grid を描く\n",
    "   plot(0,0) %原点を描く\n",
    "   axis([0, 1.2, 0, 2.2], \"square\"); %x軸の範囲を[0,1.2]、y軸の範囲を[0,2.2]にする。\n",
    "end\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#関数fを定義\n",
    "def f(x):\n",
    "    value = math.sqrt(x)+1\n",
    "    return value\n",
    "\n",
    "#グラフを描く関数を定義\n",
    "def draw_f():\n",
    "    x_list=[] \n",
    "    y_list=[]\n",
    "    for i in range(0,101):\n",
    "        x=i/100\n",
    "        x_list.append(x)\n",
    "        y_list.append(f(x))\n",
    "    plt.plot(x_list,y_list,'-r')\n",
    "    plt.grid() #グリッドを描く\n",
    "    plt.plot(0,0,'o',color='red') #原点を描く\n",
    "    \n",
    "    x_list.append(1); y_list.append(0)\n",
    "    x_list.append(0); y_list.append(0)\n",
    "    plt.fill(x_list,y_list,color=\"r\",alpha=0.2) #ピンク色で積分に対応するエリアを塗りつぶす"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#新しく作ったdraw_fという関数を呼び出して、グラフを描きます。\n",
    "draw_f()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 2.2 準備：ブロックを描く\n",
    "\n",
    "fill命令によって、長方形領域（ブロック）を緑色で塗りつぶします。\n",
    "\n",
    "> ### 塗りつぶしの方法\n",
    "> fillを使って、いくつかの点が囲んでいる範囲を指定の色と透過率で塗りつぶします。\n",
    ">\n",
    "> **使い方**：  fill(x座標のリスト, y座標のリスト, 色, 透過率)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1=0; x2=1\n",
    "y1=f(x1); y2=f(x2)\n",
    "\n",
    "#長方形の４つの頂点をリストにします。\n",
    "p1 = [x1, 0] #左下\n",
    "p2 = [x2, 0] #右下\n",
    "p3 = [x2,y2] #右上\n",
    "p4 = [x1,y2] #左上\n",
    "\n",
    "x_list = [p1[0],p2[0],p3[0],p4[0]] #x座標のリスト\n",
    "y_list = [p1[1],p2[1],p3[1],p4[1]] #y座標のリスト\n",
    "\n",
    "draw_f()\n",
    "plt.fill(x_list,y_list,color=\"g\",alpha=0.5) #緑色で長方形を塗りつぶす\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上記のコードをコンパクトにするために、ブロックを塗りつぶす関数を定義します。\n",
    "\n",
    "- draw_f_upper(x1,x2) : 区間$[x1, x2]$における$f(x)=\\sqrt{x}+1$をカバーするブロックを描く。\n",
    "- draw_f_lower(x1,x2) : 区間$[x1, x2]$における$f(x)=\\sqrt{x}+1$に囲まれるブロックを描く。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_f_upper(x1,x2):\n",
    "    y1=f(x1)\n",
    "    y2=f(x2)\n",
    "\n",
    "    x_list = [x1,x2,x2,x1] #x座標のリスト\n",
    "    y_list = [0,0,y2,y2]   #y座標のリスト\n",
    "    plt.fill(x_list,y_list,'g',alpha=0.7)\n",
    "    \n",
    "def draw_f_lower(x1,x2):\n",
    "    y1=f(x1)\n",
    "    y2=f(x2)\n",
    "\n",
    "    x_list = [x1,x2,x2,x1] #x座標のリスト\n",
    "    y_list = [0,0,y1,y1]   #y座標のリスト\n",
    "    plt.fill(x_list,y_list,'b',alpha=0.7)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "積分範囲を$[0,0.5]$と$[0.5,1]$に分けて、ブロックを描きます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5b9MmRinkRaQJCvrOatMm+PWv4f77w+N/P/axcBPTF74Q7lbVQ8NEJCIFfWdy6FAYCnn33WH+1IMHYexY+Nd/hYsvDmEvItJCCvrOYOtWKCsL3TNr14Y7Va+8Er74RRg2LNvViUiOU9Bn0yuvwF13hQeJ7dsXngj5wx/CRReFibJFRDJAQd/RamvDePef/hReeikE+uTJYYLsESOyXZ2IxJCCvqPs3Bm6Zv7rv2D9+vDI3+nTw8XVPn2yXZ2IxJiCvr1t3Aj/+Z9hBM2uXeHi6vTp4c5V3bEqIh1AQd9e3n4bbr8dHn44jJ751KfgH/4hBL2ISAdS0GdaVRXMnAlPPhnO2C+5JAT84Fx9TqSI5DoFfaZUVYXx7vPmhQusV18NX/saDBiQ7cpEJM8p6Ntq1Sq49dYwkqZHD/jyl0PA9+2b7cpERAAFfett3Ajf/3549nu3bjB1KtxwgwJeRDodBX1L7d4N//7vYRz8/v1w2WVw003qohGRTktBH9WhQ/DAA6GbZvNm+Mxn4J/+CYYOzXZlIiJHFGXikVnAZcBmd//I2EAzKwX+F2DALuAmd381tW5NatlBoNbdizJXegeqrIR//EeoqICRI+GOO8K0fCIiOSDKGf0DhIlFHmpi/TvA+e6+zcwuIUzwPTFtfbG7v9+mKrNl50747nfhvvvg2GPDqJrLL9e8qyKSU6LMMPWcmQ07wvqFaR8XESYBz31PPAHf/GboprniCvj2t+GYY7JdlYhIi1mY3rWZjULQ/66xrpsG230XGOXuN6Y+vwNsAxy4193LjrDvNGAaQEFBwfi5c+dGbcNhqqur6d2G2Za67dzJiJ/9jBOSSaoLC1n5ne+wa9SoVn9fR6iuraV3t/y63JKtNq9al52nivbtX8P2D3pm5djZkndtdmfgiTX0buWzr4qLiyub6h7PWNCbWTHwS+BT7v5Batkgd99gZicATwPfdvfnmjteUVGRV1RUNFtXY5LJJIlEolX7Mn8+XH89bNsW/rzxxjB0spNLbtpEoqAg22V0qGy1+XO3nNLhxwQoKa1k3uzxWTl2tuRdmw/UMmNmBYkpU1q1u5k1GfQZ6Ww2s9OA+4CSupAHcPcNqT83A08CEzJxvIzbty8MkfzsZ8MsTv/93+Hiaw6EvIhIc9oc9GY2FHgC+Iq7v5m2vJeZHVP3HpgMvNbW42XcmjVw9tnhEcJXXQVz5sDo0dmuSkQkY6IMr5wDJIABZrYemAl0B3D3e4AfAP2BX1qYsLpuGGUB8GRqWTfgYXf/Yzu0ofV+/3soLYUDB8JNUBddlO2KREQyLsqom2uaWX8jcGMjy1cDp7e+tHb285/DLbdAYWF4XnxhYbYrEhFpF/k3IPzQIbj55vD65CfhwQcV8iISa/l1tbG2Njx87PHHoaQkPM5AF1xFJObyJ+UOHgz98Y8/Dt/4Rhg6Ga4fiIjEWn4E/aFDYZanRx6BadPg61/PdkUiIh0mP/rop08Pz42/7roQ9CIieST+Qf/gg/CrX4Wp/aZPz3Y1IiIdLt5Bv3JleDDZqafCjBnqkxeRvBTfoN+7F77whTCq5sc/1ugaEclb8U2/m2+GFSvgrrsgzx74JSKSLp5n9Nu3w/33h0lCzj8/29WIiGRVPIO+vDyMm//857NdiYhI1sUz6J94Avr1g7FHnCdFRCQvxC7obf9++POf4dxzNberiAgxDPq+S5fC7t1wwQXZLkVEpFOIXdAPeP556NEDJk7MdikiIp1CvILenQEvvghFRXD00dmuRkSkU4gU9GY2y8w2m1mjUwFa8HMzW2Vmy8zsrLR115nZW6nXdZkqvFGVlfR4/30oLm7Xw4iI5JKoZ/QPAEeamvwSYHjqNQ34FYCZHUeYenAiYWLwmWbWr7XFNuvRR/EuXSCRaLdDiIjkmkhB7+7PAVuPsEkJ8JAHi4C+ZvZx4GLgaXff6u7bgKc58i+MtikvZ8fo0dC3b7sdQkQk12TqEQiDgHVpn9enljW1/CPMbBrhXwMUFBSQTCZbVECXvXs53Yy148/msYrtLdo31/Xtf5D71OYOUVJa2eHHBOjbvyZrx86WvGuzO9X797c4+6LoNM+6cfcyoAygqKjIE63pfjnxRJa8sJl5s8dntrhOrqS0Um2OuXxrL+Rhmw/UMmNmBa3KvmZkatTNBmBI2ufBqWVNLW8/ehSxiMhhMhX05cBXU6NvzgZ2uPtGYAEw2cz6pS7CTk4tExGRDhKp68bM5gAJYICZrSeMpOkO4O73APOBS4FVQA3wtdS6rWZ2O7Ak9VW3ufuRLuqKiEiGRQp6d7+mmfUOfKuJdbOAWS0vTUREMiFed8aKiMhHKOhFRGJOQS8iEnMKehGRmFPQi4jEnIJeRCTmFPQiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZhT0IuIxJyCXkQk5hT0IiIxp6AXEYm5SEFvZlPMbKWZrTKz7zWy/mdmtjT1etPMtqetO5i2rjyDtYuISATNzjBlZl2Bu4GLgPXAEjMrd/cVddu4+y1p238bODPtK/a4+xkZq1hERFokyhn9BGCVu6929/3AXKDkCNtfA8zJRHEiItJ2FqZ7PcIGZlcBU9z9xtTnrwAT3X16I9sWAouAwe5+MLWsFlgK1AJ3uvtTTRxnGjANoKCgYPzcuXNb3po9e3i/upbtW3u2fN8c1rd/Dds/UJvjLN/aC3nYZncGnlhD7z59WrV7cXFxpbsXNbYu0uTgLTAVeKwu5FMK3X2DmZ0M/NXMlrv72w13dPcyoAygqKjIE4lEy4++bBn3LdzCvIfHt6r4XFVSWsm82WpznOVbeyEP23yglhkzK2hV9jUjStfNBmBI2ufBqWWNmUqDbht335D6czWQ5PD+exERaWdRgn4JMNzMTjKzowhh/pHRM2Y2CugHvJi2rJ+Z9Ui9HwCcB6xouK+IiLSfZrtu3L3WzKYDC4CuwCx3rzKz24AKd68L/anAXD+80380cK+ZHSL8UrkzfbSOiIi0v0h99O4+H5jfYNkPGnz+YSP7LQTGtaE+ERFpI90ZKyIScwp6EZGYU9CLiMScgl5EJOYU9CIiMaegFxGJOQW9iEjMKehFRGJOQS8iEnMKehGRmFPQi4jEnIJeRCTmFPQiIjGnoBcRiTkFvYhIzEUKejObYmYrzWyVmX2vkfXXm9kWM1uaet2Ytu46M3sr9bouk8WLiEjzmp14xMy6AncDFwHrgSVmVt7ITFG/cffpDfY9DpgJFAEOVKb23ZaR6kVEpFlRzugnAKvcfbW77wfmAiURv/9i4Gl335oK96eBKa0rVUREWiPKVIKDgHVpn9cDExvZ7koz+wzwJnCLu69rYt9BjR3EzKYB0wAKCgpIJpMRSmtgzx769q+lpLSy5fvmsL79a9TmmMu39kIettmd6v37W5d9zYg0Z2wEvwXmuPs+M/sG8CBwQUu+wN3LgDKAoqIiTyQSLa9i2TLuW7iFeQ+Pb/m+OayktJJ5s9XmOMu39kIetvlALTNmVtCq7GtGlK6bDcCQtM+DU8s+5O4fuPu+1Mf7gPFR9xURkfYVJeiXAMPN7CQzOwqYCpSnb2BmH0/7eDnweur9AmCymfUzs37A5NQyERHpIM123bh7rZlNJwR0V2CWu1eZ2W1AhbuXA98xs8uBWmArcH1q361mdjvhlwXAbe6+tR3aISIiTYjUR+/u84H5DZb9IO39rcCtTew7C5jVhhpFRKQNdGesiEjMKehFRGJOQS8iEnMKehGRmFPQi4jEnIJeRCTmFPQiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZhT0IuIxJyCXkQk5hT0IiIxp6AXEYm5SEFvZlPMbKWZrTKz7zWy/p/NbIWZLTOzv5hZYdq6g2a2NPUqb7iviIi0r2ZnmDKzrsDdwEXAemCJmZW7+4q0zV4Bity9xsxuAn4MfCm1bo+7n5HZskVEJKooZ/QTgFXuvtrd9wNzgZL0Ddz9GXevSX1cBAzObJkiItJa5u5H3sDsKmCKu9+Y+vwVYKK7T29i+18A77n7j1Kfa4GlhInD73T3p5rYbxowDaCgoGD83LlzW96aPXt4v7qW7Vt7tnzfHNa3fw3bP1Cb4yzf2gt52GZ3Bp5YQ+8+fVq1e3FxcaW7FzW2LtLk4FGZ2bVAEXB+2uJCd99gZicDfzWz5e7+dsN93b0MKAMoKiryRCLR8gKWLeO+hVuY9/D41pSfs0pKK5k3W22Os3xrL+Rhmw/UMmNmBa3KvmZE6brZAAxJ+zw4tewwZnYh8H3gcnffV7fc3Tek/lwNJIEz21CviIi0UJSgXwIMN7OTzOwoYCpw2OgZMzsTuJcQ8pvTlvczsx6p9wOA84D0i7giItLOmu26cfdaM5sOLAC6ArPcvcrMbgMq3L0c+AnQG3jUzADedffLgdHAvWZ2iPBL5c4Go3VERKSdReqjd/f5wPwGy36Q9v7CJvZbCIxrS4EiItI2ujNWRCTmFPQiIjGnoBcRiTkFvYhIzCnoRURiTkEvIhJzCnoRkZhT0IuIxJyCXkQk5hT0IiIxp6AXEYk5Bb2ISMwp6EVEYk5BLyIScwp6EZGYU9CLiMRcpKA3sylmttLMVpnZ9xpZ38PMfpNav9jMhqWtuzW1fKWZXZzB2g83ezZMmcINN13E/S+N4/zNj7bboUREckmzQW9mXYG7gUuAMcA1ZjamwWY3ANvc/RPAz4D/SO07hjDH7KnAFOCXqe/LrNmzYdo02LgRwzlh33qmv3Wzwl5EhGhTCU4AVrn7agAzmwuUcPgk3yXAD1PvHwN+YWHy2BJgrrvvA94xs1Wp73sxM+WnfP/7UFNz2KKjD+3hq+/cxrPHlmT0UJ2SO+zbn+0qOla+tTnf2gv512Y/1G5fHSXoBwHr0j6vByY2tU1qMvEdQP/U8kUN9h3U2EHMbBowDaCgoIBkMhmhtOD8d9/FGll+/IENzLhjWeTvyVXVe/bkRTvT5Vub8629kK9tPtCi7Isq0uTgHcHdy4AygKKiIk8kEtF3HjoU1q79yGIbOpTEhY3OWx4ryWSSFv19xUC+tTnf2gtqcyZFuRi7ARiS9nlwalmj25hZN+BY4IOI+7bdHXdAz56HL+vZMywXEclzUYJ+CTDczE4ys6MIF1fLG2xTDlyXen8V8Fd399TyqalROScBw4GXMlN6mtJSKCuDwkLcDAoLw+fS0owfSkQk1zTbdZPqc58OLAC6ArPcvcrMbgMq3L0cuB/4f6mLrVsJvwxIbfcI4cJtLfAtdz/YLi0pLYXSUp7Nw3/uiYgcSaQ+enefD8xvsOwHae/3Alc3se8dgPpQRESyRHfGiojEnIJeRCTmFPQiIjGnoBcRiTkLoyA7FzPbAnz0DqhoBgDvZ7CcXKA2x1++tRfU5pYqdPfjG1vRKYO+Lcyswt2Lsl1HR1Kb4y/f2gtqcyap60ZEJOYU9CIiMRfHoC/LdgFZoDbHX761F9TmjIldH72IiBwujmf0IiKSRkEvIhJzORv0bZmwPBdFaO8/m9kKM1tmZn8xs8Js1JlJzbU5bbsrzczNLOeH4kVps5l9MfWzrjKzhzu6xkyL8N/2UDN7xsxeSf33fWk26swUM5tlZpvN7LUm1puZ/Tz197HMzM5q80HdPedehMclvw2cDBwFvAqMabDNN4F7Uu+nAr/Jdt3t3N5ioGfq/U253N6obU5tdwzwHGHKyqJs190BP+fhwCtAv9TnE7Jddwe0uQy4KfV+DLAm23W3sc2fAc4CXmti/aXAHwADzgYWt/WYuXpG/+GE5e6+H6ibsDxdCfBg6v1jwKTUhOW5qNn2uvsz7l43Q/oiwmxeuSzKzxjgduA/gL0dWVw7idLmrwN3u/s2AHff3ME1ZlqUNjvQJ/X+WODvHVhfxrn7c4R5O5pSAjzkwSKgr5l9vC3HzNWgb2zC8oaTjh82YTlQN2F5LorS3nQ3EM4IclmzbU79k3aIu/++IwtrR1F+ziOAEWb2gpktMrMpHVZd+4jS5h8C15rZesK8GN/umNKypqX/vzer00wOLplhZtcCRcD52a6lPZlZF+CnwPVZLqWjdSN03yQI/2p7zszGufv2bBbVzq4BHnD3u8zsHMJsdmPd/VC2C8sVuXpG35YJy3NRpEnWzexC4PvA5e6+r4Nqay/NtfkYYCyQNLM1hL7M8hy/IBvl57weKHf3A+7+DvAmIfhzVZQ23wA8AuDuLwJHEx7+FVeR/n9viVwN+rZMWJ6Lmm2vmZ0J3EsI+Vzvt4Vm2uzuO9x9gLsPc/dhhOsSl7t7RXbKzYgo/10/RTibx8wGELpyVndgjZkWpc3vApMAzGw0Iei3dGiVHasc+Gpq9M3ZwA5339iWL8zJrhtvw4TluShie38C9AYeTV1zftfdL89a0W0Usc2xErHNC4DJZrYCOAj8i7vn6r9Uo7Z5BvBrM7uFcGH2+hw+acPM5hB+WQ9IXXeYCXQHcPd7CNchLgVWATXA19p8zBz++xIRkQhytetGREQiUtCLiMScgl5EJOYU9CIiMaegFxGJOQW9iEjMKehFRGLu/wNQqbTQX2OVyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "draw_f()\n",
    "draw_f_upper(0, 0.5)\n",
    "draw_f_upper(0.5, 1)\n",
    "\n",
    "plt.figure(2)\n",
    "draw_f()\n",
    "draw_f_lower(0, 0.5)\n",
    "draw_f_lower(0.5, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 面積の計算法\n",
    "\n",
    "ブロックの面積によって、積分値の上界と下界を算出することができます。\n",
    "\n",
    "$[0,1]$の分割点$x=0,0.5,1$におけるブロックの面積を検討してみます。このとき、各小区間の幅は$h=0.5$です。\n",
    "\n",
    "- 青色のブロックの面積は積分値の下界を与えます。$S1$と書きます。\n",
    "$$ S1 = h\\cdot [ \\, f(0) + f(0.5)\\, ] $$\n",
    "- 緑色のブロックの面積は積分値の上界を与えます。$S2$と書きます。\n",
    "$$ S2 = h\\cdot [ \\, f(0.5) + f(1)\\, ] $$\n",
    "\n",
    "\n",
    "\n",
    "### 演習1 \n",
    "\n",
    "分割点が$x=0,0.5,1$の場合に、\n",
    "青色のブロックの面積$S1$と緑色のブロックの面積$S2$を計算しなさい。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#演習1の計算過程を書いてください。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 演習2\n",
    "\n",
    "$[0,1]$の$10$等分割を考えます。積分領域をカバーする緑色のブロックと、積分領域に囲まれる青色のブロックを描いてみます。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#演習2\n",
    "\n",
    "n=10; h=1/n\n",
    "\n",
    "plt.figure(1)\n",
    "draw_f()\n",
    "for k in range(0,n):\n",
    "    draw_f_upper(k*h, k*h+h)\n",
    "\n",
    "plt.figure(2)\n",
    "draw_f()\n",
    "for k in range(0,n):\n",
    "    draw_f_lower(k*h, k*h+h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "描いた緑色のブロックの面積$S2$と青色のブロックの面積$S1$を計算しなさい。それぞれ、積分値の上界と下界になります。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S1 is: 1.6105093417068177\n"
     ]
    }
   ],
   "source": [
    "#ここに計算の過程を書いてください。\n",
    "#ヒントとして、S1の計算法を用意しています。S2の計算法を考えてください。\n",
    "\n",
    "h = 0.1\n",
    "S1 = 0.0\n",
    "for n in range(0,10):\n",
    "    x = n*h\n",
    "    S1 = S1 + h*f(x)\n",
    "    \n",
    "print(\"S1 is:\", S1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 演習3  (オプション)\n",
    "\n",
    "積分値の上界($S2$)と下界($S1$)の差が$0.01$以下に収まるように、$[0,1]$の分割点を調整して、$S1$, $S2$を計算してください。即ち、計算される$S1$, $S2$については，$S2-S1\\leq 0.01$を満たすことが要求されています。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#演習3\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 一般的な関数の積分\n",
    "\n",
    "### 演習4 (オプション)\n",
    "\n",
    "この授業で紹介した方法を利用して、以下の関数の$[0,1]$における積分の近似値を計算してみてください。\n",
    "分割の点で関数の値が発散する場合、分割の小区間の中点を使って計算してください。\n",
    "\n",
    "\n",
    "**注意：**\n",
    "\n",
    "関数の積分の上界と下界を得るためには、関数の単調性が大切です。以下の３番目と４番目の関数について、\n",
    "分割の各小区間$[x_i,x_{i+1}]$上での関数の単調性を確保するために、区間の分割に工夫が必要です。\n",
    "\n",
    "関数の単調性を調べるのが難しい場合、与えられる分割におけるリーマン和を計算して、リーマン和が収束しているかどうかを考察してください。\n",
    "\n",
    "$$f_1(x)=\\frac{1}{\\sqrt{x}}$$\n",
    "\n",
    "$$f_2(x)=\\frac{1}{x}$$\n",
    "\n",
    "$$f_3(x)=x\\sin \\frac{1}{x}$$\n",
    "\n",
    "$$f_4(x)=\\sin \\frac{1}{x}$$\n",
    "\n",
    "> ## リーマン和\n",
    "> 分割$x_0=0 < x_1 <x_2 < \\cdots < x_n=1$に対して、$t_i$を$[x_i,x_{i+1}]$の中に存在する点とします。例えば、$t_i=0.5*(x_i+x_{i+1})$。この場合、リーマン和は以下のように計算できます。\n",
    "> $$ \\sum^{n-1}_{i=0}  f(t_i) (x_{i+1} - x_{i} ) $$\n",
    ">\n",
    ">（参考：[https://ja.wikipedia.org/wiki/%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3%E7%A9%8D%E5%88%86](https://ja.wikipedia.org/wiki/%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3%E7%A9%8D%E5%88%86)）\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ここにコードを書いてください。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 参考\n",
    "\n",
    "### 積分の厳密な定義（リーマン積分）\n",
    "\n",
    "微分積分の授業で学んだリーマン積分は積分を厳密に定義します。その詳細は教科書または[Wikipedia](https://ja.wikipedia.org/wiki/%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3%E7%A9%8D%E5%88%86)を参照してください。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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