![\"\"](\"https:\/\/www.educational-lounge.com\/wp-content\/uploads\/2020\/06\/pexels-photo-3781338-300x199.jpeg\")
<\/p>\n\u3069\u3046\u3082, \u307f\u306a\u3055\u3093\u3053\u3093\u306b\u3061\u306f\u3002
\n\u9ad8\u6a4b\u4f73\u4f51\u3067\u3059\u3002<\/p>\n
\u4eca\u56de\u306f\u6570\u5b66\u2162\u306e\u516c\u5f0f\u3068\u306e\u5411\u304d\u5408\u3044\u65b9\u306b\u3064\u3044\u3066\u304a\u8a71\u3057\u307e\u3059\u3002
\nIAIIB\u306e\u516c\u5f0f\u3068\u30ea\u30f3\u30af\u3059\u308b\u3082\u306e\u3042\u308b\u306e\u3067, \u4f3c\u305f\u5f0f\u3092\u898b\u305f\u3089\u305d\u306e\u5206\u91ce\u3092\u632f\u308a\u8fd4\u3063\u3066\u307f\u308b\u3068\u826f\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n
\u9ad8\u6821\u6570\u5b66\u5168\u822c\u3067\u8a00\u3048\u308b\u3053\u3068\u3067\u3059\u304c, \u6587\u5b57\u306e\u307e\u307e\u4f55\u5ea6\u3082\u66f8\u304f, \u3042\u308b\u3044\u306f\u5fa9\u5531\u3057\u3066\u899a\u3048\u3066\u3082\u4f7f\u3048\u308b\u3088\u3046\u306b\u306f\u306a\u308a\u307e\u305b\u3093\u3002
\n\u516c\u5f0f\u306e\u610f\u5473\u3092\u8003\u3048\u7406\u89e3\u3059\u308b\u3068\u899a\u3048\u3084\u3059\u304f\u3082\u306a\u308a\u307e\u3059\u3057, \u4f7f\u3044\u3084\u3059\u304f\u3082\u306a\u308a\u307e\u3059\u3002
\n\u4eca\u56de\u306f\u3044\u304f\u3064\u304b\u306e\u516c\u5f0f\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n
<\/p>\n
IAIIB\u306e\u516c\u5f0f\u306e\u4e2d\u306b<\/p>\n
\u5186$x^2 +y^2 =r^2$\u4e0a\u306e\u70b9 $(x_0 ,y_0)$\u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f$$x_0 x + y_0 y = r^2$$<\/p>\n
\u3067\u4e0e\u3048\u3089\u308c\u308b\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002
\n\u306a\u305c, \u3053\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u304b\u306f\u6570\u5b66\u2161\u306e\u56f3\u5f62\u3068\u65b9\u7a0b\u5f0f\u306e\u5358\u5143\u3092\u5fa9\u7fd2\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n
<\/p>\n
\u6570\u5b66\u2162\u3067\u306f\u6955\u5186\u3068\u53cc\u66f2\u7dda\u3092\u5b66\u7fd2\u3057\u307e\u3059\u304c, \u4e0a\u3068\u540c\u69d8\u306b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306e\u516c\u5f0f\u304c\u3042\u308b\u306e\u3067\u95a2\u9023\u4ed8\u3051\u3066\u899a\u3048\u3066\u3057\u307e\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n
\u5186\u5468\u4e0a\u306e\u70b9\u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u516c\u5f0f\u306f$x^2 , y^2$\u3092$x\u00d7x, y\u00d7y$\u3068\u3057\u3066$1$\u3064\u306e$x, y$\u3092\u305d\u308c\u305e\u308c\u63a5\u70b9\u306e\u5ea7\u6a19\u306b\u5909\u3048\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n
\u540c\u69d8\u306b\u8003\u3048\u308b\u3068,<\/p>\n
\u6955\u5186$\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1$\u4e0a\u306e\u70b9$(x_0, y_0)$\u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f$$\\frac{x_0}{a^2}x+\\frac{y_0}{b^2}y=1$$\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n
\u53cc\u66f2\u7dda$\\frac{x^2}{a^2}-\\frac{y^2}{b^2}=\\pm1$\u4e0a\u306e\u70b9$(x_0, y_0)$\u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f$$\\frac{x_0}{a^2}x-\\frac{y_0}{b^2}y=\\pm1$$\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n
\u4e2d\u5fc3\u304c\u305a\u308c\u305f\u3082\u306e\u306b\u95a2\u3057\u3066\u3082\u540c\u69d8\u306b\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n
<\/p>\n
![\"\u6570\u5b66\u306e\u5206\u539a\u3044\u554f\u984c\u96c6\u306f\u300c\u554f\u984c\u8f9e\u66f8\u300d\u3068\u3057\u3066\u5229\u7528\u3057\u3088\u3046\"](\"https:\/\/www.educational-lounge.com\/wp-content\/uploads\/2020\/06\/pexels-photo-167682-300x200.jpeg\")
<\/p>\n
\u533a\u5206\u6c42\u7a4d\u6cd5\u306e\u516c\u5f0f\u306f<\/p>\n
$$\\lim_{n \\to \\infty}\\frac{1}{n}\\sum_{k=0}^{n-1} f(\\frac{k}{n})=\\int_{0}^{1}f(x)dx$$ $$\\lim_{n \\to \\infty}\\frac{1}{n}\\sum_{k=1}^n f(\\frac{k}{n})=\\int_{0}^{1}f(x)dx$$<\/p>\n
\u306e$2$\u3064\u304c\u6559\u79d1\u66f8\u3067\u7d39\u4ecb\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n
\u3053\u308c\u306f$y = f(x)$\u306e\u30b0\u30e9\u30d5\u3068$x$\u8ef8$,y$\u8ef8 \u304a\u3088\u3073\u76f4\u7dda$x=1$\u3067\u56f2\u307e\u308c\u308b\u90e8\u5206\u306e\u9762\u7a4d\u3068\u8003\u3048\u308b\u3068\u7d0d\u5f97\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n
\u533a\u9593$[0, 1]$\u3092$n$\u7b49\u5206\u3057\u9577\u65b9\u5f62\u3092\u4f5c\u308b\u3002 \u56f3$1\uff1ak = 0, 1, 2, \\cdots\\cdots , n \u2212 1$ \u3068\u306a\u308b\u304b\u3089,$n$\u3092\u9650\u308a\u306a\u304f\u5927\u304d\u304f\u3057\u3066\u9577\u65b9\u5f62\u3092\u7d30\u304b\u304f\u5206\u3051\u3066\u3044\u304f\u3068\u533a\u5206\u6c42\u7a4d\u306e\u516c\u5f0f<\/p>\n $$\\lim_{n \\to \\infty}\\sum_{k=0}^{n-1} \\frac{1}{n}f(\\frac{k}{n})=\\int_{0}^{1}f(x)dx$$ $$\\lim_{n \\to \\infty}\\sum_{k=1}^n \\frac{1}{n}f(\\frac{k}{n})=\\int_{0}^{1}f(x)dx$$<\/p>\n \u3092\u5f97\u307e\u3059\u3002<\/p>\n \u5148\u306b\u7d39\u4ecb\u3057\u305f\u516c\u5f0f\u3068$\\frac{1}{n}$\u306e\u4f4d\u7f6e\u304c\u9055\u3046\u3053\u3068\u306b\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002 \u3067\u306f\u5c11\u3057\u30ec\u30d9\u30eb\u3092\u4e0a\u3052\u3066, \u533a\u5206\u6c42\u7a4d\u6cd5\u306b\u304a\u3044\u3066$k$\u306e\u53d6\u308b\u5024\u3092\u5909\u3048, \u7a4d\u5206\u533a\u9593\u3092\u5909\u3048\u3066\u898b\u307e\u3057\u3087\u3046\u3002<\/p>\n $$I_1 =\\lim_{n \\to \\infty}\\frac{1}{n}\\sum_{k=0}^{2n-1} f(\\frac{k}{n})$$ $$I_2 =\\lim_{n \\to \\infty}\\frac{1}{n}\\sum_{k=n+1}^{3n} f(\\frac{k}{n})$$<\/p>\n \u3053\u308c\u3089\u306f\u4e0a\u306e\u533a\u5206\u6c42\u7a4d\u306e\u516c\u5f0f\u306e\u6210\u308a\u7acb\u3061\u3092\u8003\u3048\u308b\u3053\u3068\u3067\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n \u3069\u306e\u3088\u3046\u306b\u7a4d\u5206\u533a\u9593\u304c\u5909\u308f\u308b\u304b\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002 $$I_1 =\\lim_{n \\to \\infty}\\frac{1}{n}\\sum_{k=0}^{2n-1} f(\\frac{k}{n})=\\int_{0}^{2}f(x)dx$$<\/p>\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n
\n![\"\"](\"https:\/\/www.educational-lounge.com\/wp-content\/uploads\/2021\/12\/54af0743ca0aeedc4b326268cdbce25b-1-300x188.png\")
<\/a>
\n\u56f3$1$\u3067\u306f\u76f4\u7dda$x=\\frac{k}{n}$\u306e\u53f3\u5074\u306b, \u56f3$2$\u3067\u306f\u76f4\u7dda$x=\\frac{k}{n}$\u306e\u5de6\u5074\u306b\u9577\u65b9\u5f62\u3092\u4f5c\u308b\u3002
\n\u3069\u3061\u3089\u306e\u56f3\u306b\u304a\u3044\u3066\u3082\u3053\u306e\u9577\u65b9\u5f62\u306e\u9762\u7a4d\u306f$\\frac{1}{n}f(\\frac{k}{n})$\u3068\u306a\u308b\u3002
\n<\/a>
\n$k$\u306e\u53d6\u308b\u5024\u306e\u7bc4\u56f2\u3092\u898b\u308b\u3068,<\/p>\n
\n\u56f3$2\uff1ak = 1, 2, 3, \\cdots\\cdots , n$<\/p>\n
\n\u9577\u65b9\u5f62\u3092\u96c6\u3081\u3066$n$\u3092\u7121\u9650\u5927\u306b\u3059\u308b\u3068\u3044\u3046\u516c\u5f0f\u306e\u6210\u308a\u7acb\u3061\u3092\u8003\u3048\u308b\u3068, \u5f8c\u306b\u7d39\u4ecb\u3057\u305f\u516c\u5f0f\u304c\u81ea\u7136\u306b\u899a\u3048\u3089\u308c\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n
\n$I_1$\u306b\u3064\u3044\u3066,$\\frac{1}{n}f(\\frac{k}{n})$\u306f\u4e0a\u3067\u8003\u3048\u305f\u9577\u65b9\u5f62\u306e\u9762\u7a4d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002
\n$k$ \u306e\u5024\u304c$0$\u304b\u3089$2n \u2212 1$\u307e\u3067\u5909\u5316\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u306f,
\n<\/a><\/p>\n