{"id":11586,"date":"2022-12-14T22:45:12","date_gmt":"2022-12-14T13:45:12","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11586"},"modified":"2022-12-18T06:34:39","modified_gmt":"2022-12-17T21:34:39","slug":"integral-2","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/integral-2.html","title":{"rendered":"\u7a4d\u5206\u3067\u306e\u9762\u7a4d\u8a08\u7b97\uff1a\u63a5\u7dda\u3084\u7d76\u5bfe\u5024\u30016\u5206\u306e1\u516c\u5f0f\u3001\u6700\u5927\u30fb\u6700\u5c0f"},"content":{"rendered":"\n<p>\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u304c\u7a4d\u5206\u3067\u3059\u3002\u305d\u3053\u3067\u66f2\u7dda\u306b\u3064\u3044\u3066\u3001\u5b9a\u7a4d\u5206\u3092\u7528\u3044\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x\\)\u8ef8\u3068\u66f2\u7dda\u306b\u3088\u308b\u9762\u7a4d\u3092\u8a08\u7b97\u3057\u305f\u3044\u5834\u5408\u3001\\(y\\)\u8ef8\u306e\u5024\u304c\u30d7\u30e9\u30b9\u306b\u306a\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u306e\u304b\u306b\u3088\u3063\u3066\u7b26\u53f7\u3092\u8003\u3048\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u307e\u305f2\u66f2\u7dda\u306e\u9593\u306e\u9762\u7a4d\u3067\u306f\u3001\u3069\u3061\u3089\u306e\u66f2\u7dda\u3067\\(y\\)\u8ef8\u306e\u5024\u304c\u5927\u304d\u304f\u306a\u308b\u306e\u304b\u3092\u8003\u3048\u3066\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u7a4d\u5206\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u9762\u7a4d\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u307b\u304b\u306b\u3082\u3001\u5f0f\u306b\u7d76\u5bfe\u5024\u3092\u542b\u3080\u5834\u5408\u306e\u7a4d\u5206\u306b\u3064\u3044\u3066\u3082\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u3069\u306e\u3088\u3046\u306b\u7a4d\u5206\u3057\u3001\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u66f2\u7dda\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u9762\u7a4d\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u66f2\u7dda\u3068\\(x\\)\u8ef8\u306b\u3088\u308b\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u7bc4\u56f2\u3092\u6307\u5b9a\u3057\u3066\u7a4d\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u9762\u7a4d\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u66f2\u7dda\u3068\\(x\\)\u8ef8\u306e\u9593\u306b\u4f5c\u3089\u308c\u308b\u9762\u7a4d\u306b\u3064\u3044\u3066\u3001\u7bc4\u56f2\u304c\\(a\\)\u304b\u3089\\(b\\)\u306e\u5834\u5408\u3001\u9762\u7a4d\\(S\\)\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(S=\\displaystyle \\int_{a}^{b} f(x) dx\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/ekej6.jpg\" alt=\"\" width=\"459\" height=\"294\" class=\"aligncenter size-full wp-image-11590\" \/><\/p>\n<p>\u5b9a\u7a4d\u5206\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u9762\u7a4d\u306e\u8a08\u7b97\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<p>\u305f\u3060\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\\(x\\)\u8ef8\u306e\u4e0b\u5074\u306b\u95a2\u6570\u304c\u5b58\u5728\u3059\u308b\u30b1\u30fc\u30b9\u3082\u3042\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\\(a\u2266x\u2266b\\)\u306e\u7bc4\u56f2\u3067\\(y\\)\u306e\u5024\u304c\u30de\u30a4\u30ca\u30b9\u306e\u5834\u5408\u3001\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u306b\u30de\u30a4\u30ca\u30b9\u3092\u52a0\u3048\u307e\u3057\u3087\u3046\u3002<\/span>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(S=-\\displaystyle \\int_{a}^{b} f(x) dx\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fwh2-1.jpg\" alt=\"\" width=\"534\" height=\"297\" class=\"aligncenter size-full wp-image-11592\" \/><\/p>\n<p>\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u5834\u6240\u306b\u3088\u3063\u3066\\(y\\)\u8ef8\u306e\u5024\u304c\u30d7\u30e9\u30b9\u306b\u306a\u3063\u305f\u308a\u3001\u30de\u30a4\u30ca\u30b9\u306b\u306a\u3063\u305f\u308a\u3068\u5909\u5316\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\\(y\\)\u8ef8\u306e\u5024\u304c\u30de\u30a4\u30ca\u30b9\u306e\u3068\u304d\u306e\u307f\u3001\u7a4d\u5206\u3059\u308b\u3068\u304d\u306b\u30de\u30a4\u30ca\u30b9\u3092\u52a0\u3048\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(S=\\displaystyle \\int_{a}^{b} f(x) dx\\)\\(-\\displaystyle \\int_{b}^{c} f(x) dx\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fwh3.jpg\" alt=\"\" width=\"438\" height=\"266\" class=\"aligncenter size-full wp-image-11593\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\u4ee5\u4e0b\u306e\u5f0f\u306b\u3064\u3044\u3066\u3001\\(-1\u2266x\u22661\\)\u306e\u3068\u304d\u3001\u66f2\u7dda\u3068\\(x\\)\u8ef8\u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(y=x^2-3x\\)<\/li>\n<\/ul>\n<p>\u9762\u7a4d\u306e\u8a08\u7b97\u3067\u306f\u3001\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u56e0\u6570\u5206\u89e3\u3059\u308b\u3068\u3001\\(y=x(x-3)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(x\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u306f\\(0,3\\)\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fjeh1.jpg\" alt=\"\" width=\"408\" height=\"240\" class=\"aligncenter size-full wp-image-11596\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\u30b0\u30e9\u30d5\u3092\u5229\u7528\u3057\u3066\u3001\\(y\\)\u8ef8\u306e\u5024\u304c\u30d7\u30e9\u30b9\u306b\u306a\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u306e\u304b\u3092\u78ba\u8a8d\u3057\u3066\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{0} (x^2-3x) dx\\)\\(-\\displaystyle \\int_{0}^{1} (x^2-3x) dx\\)<\/p>\n<p>\\(S=\\left[\\displaystyle\\frac{1}{3}x^3-\\displaystyle\\frac{3}{2}x^2\\right]_{-1}^{0}\\)\\(-\\left[\\displaystyle\\frac{1}{3}x^3-\\displaystyle\\frac{3}{2}x^2\\right]_{0}^{1}\\)<\/p>\n<p>\\(S=0-\\left(-\\displaystyle\\frac{1}{3}-\\displaystyle\\frac{3}{2}\\right)\\)\\(-\\left(\\displaystyle\\frac{1}{3}-\\displaystyle\\frac{3}{2}\\right)+0\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{11}{6}+\\displaystyle\\frac{7}{6}\\)<\/p>\n<p>\\(S=3\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u9762\u7a4d\u306f\\(S=3\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>2\u66f2\u7dda\u306e\u9593\u306e\u9762\u7a4d\u3068\u7a4d\u5206<\/h3>\n<p>\u305d\u308c\u3067\u306f\u66f2\u7dda\u3068\\(x\\)\u8ef8\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u9762\u7a4d\u3067\u306f\u306a\u304f\u30012\u66f2\u7dda\u306e\u9593\u306e\u9762\u7a4d\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u3068\u306f\u7570\u306a\u308a\u3001<span style=\"color: #0000ff;\">\\(y\\)\u8ef8\u306e\u7b26\u53f7\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u306f\u306a\u304f\u30012\u3064\u306e\u66f2\u7dda\u306b\u3064\u3044\u3066\u3001\u5f15\u304d\u7b97\u3092\u3057\u3066\u7a4d\u5206\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002<\/span><\/p>\n<p>\u4f8b\u3048\u3070\\(a\\)\u304b\u3089\\(b\\)\u306e\u7bc4\u56f2\u3067\\(f(x)&gt;g(x)\\)\u3067\u3042\u308b2\u3064\u306e\u95a2\u6570\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u30012\u3064\u306e\u95a2\u6570\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\\(a\\)\u304b\u3089\\(b\\)\u307e\u3067\u306e\u9762\u7a4d\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(S=\\displaystyle \\int_{a}^{b} \\{f(x)-g(x)\\} dx\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fjeh2.jpg\" alt=\"\" width=\"408\" height=\"239\" class=\"aligncenter size-full wp-image-11599\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(y=x^2\\)\u3068\\(y=-x^2-x+1\\)\u306b\u3088\u3063\u3066\u56f2\u307e\u308c\u308b\u9762\u7a4d\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u30012\u3064\u306e\u66f2\u7dda\u306e\u4ea4\u70b9\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x^2=-x^2-x+1\\)<\/p>\n<p>\\(2x^2+x-1=0\\)<\/p>\n<p>\\((2x-1)(x+1)=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\\(x=-1,\\displaystyle\\frac{1}{2}\\)\u306e\u3068\u304d\u30012\u66f2\u7dda\u306f\u4ea4\u308f\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fjeh3.jpg\" alt=\"\" width=\"519\" height=\"308\" class=\"aligncenter size-full wp-image-11606\" \/><\/p>\n<p>\u307e\u305f\u3001\\(-1\u2266x\u2266\\displaystyle\\frac{1}{2}\\)\u3067\u306f\\(y=-x^2-x+1\\)\u304c\\(y=x^2\\)\u3088\u308a\u3082\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{\\frac{1}{2}} \\{(-x^2-x+1)-(x^2)\\} dx\\)<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{\\frac{1}{2}} (-2x^2-x+1) dx\\)<\/p>\n<p>\\(S=\\left[-\\displaystyle\\frac{2}{3}x^3-\\displaystyle\\frac{1}{2}x^2+x\\right]_{-1}^{\\frac{1}{2}}\\)<\/p>\n<p>\\(S=\\left(-\\displaystyle\\frac{1}{12}-\\displaystyle\\frac{1}{8}+\\displaystyle\\frac{1}{2}\\right)-\\left(\\displaystyle\\frac{2}{3}-\\displaystyle\\frac{1}{2}-1\\right)\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{27}{24}\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{9}{8}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u30012\u66f2\u7dda\u306e\u9593\u306e\u9762\u7a4d\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u30022\u3064\u306e\u66f2\u7dda\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u4e0a\u304b\u3089\u4e0b\u3092\u5f15\u3044\u3066\u7a4d\u5206\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u7a4d\u5206\u306b\u3088\u308b\u4e09\u6b21\u95a2\u6570\u306e\u9762\u7a4d\u306e\u8a08\u7b97<\/h3>\n<p>\u7a4d\u5206\u306b\u3088\u308b\u8a08\u7b97\u65b9\u6cd5\u306f\u4e09\u6b21\u66f2\u7dda\uff08\u4e09\u6b21\u95a2\u6570\uff09\u3067\u3042\u3063\u3066\u3082\u540c\u69d8\u3067\u3059\u3002\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u3001\u4e0a\u304b\u3089\u4e0b\u3092\u5f15\u304f\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u4e09\u6b21\u66f2\u7dda\u3068\\(x\\)\u8ef8\u306b\u3088\u308b\u9762\u7a4d\u3067\u306f\u3001\\(y\\)\u8ef8\u306e\u5024\u304c\u30d7\u30e9\u30b9\u306a\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u30de\u30a4\u30ca\u30b9\u306a\u306e\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(y=x^3-x\\)\u3068\\(x\\)\u8ef8\u3067\u56f2\u307e\u308c\u305f\u9762\u7a4d\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\(x\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u78ba\u8a8d\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(x^3-x=0\\)<\/p>\n<p>\\(x(x^2-1)=0\\)<\/p>\n<p>\\(x(x-1)(x+1)=0\\)<\/p>\n<p>\\(x=-1,0,1\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u56f3\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fjeh4.jpg\" alt=\"\" width=\"424\" height=\"314\" class=\"aligncenter size-full wp-image-11607\" \/><\/p>\n<p>\u8a08\u7b97\u65b9\u6cd5\u306f\u3053\u308c\u307e\u3067\u8aac\u660e\u3057\u305f\u3084\u308a\u65b9\u3068\u540c\u3058\u3067\u3059\u3002\u7a4d\u5206\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3082\u306e\u306e\u3001\\(y\\)\u306e\u5024\u304c\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u5834\u5408\u3001\u30de\u30a4\u30ca\u30b9\u3092\u52a0\u3048\u3066\u7a4d\u5206\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{0} (x^3-x) dx\\)\\(-\\displaystyle \\int_{0}^{1} (x^3-x) dx\\)<\/p>\n<p>\\(S=\\left[\\displaystyle\\frac{1}{4}x^4-\\displaystyle\\frac{1}{2}x^2\\right]_{-1}^{0}\\)\\(-\\left[\\displaystyle\\frac{1}{4}x^4-\\displaystyle\\frac{1}{2}x^2\\right]_{0}^{1}\\)<\/p>\n<p>\\(S=0-\\left(\\displaystyle\\frac{1}{4}-\\displaystyle\\frac{1}{2}\\right)\\)\\(-\\left(\\displaystyle\\frac{1}{4}-\\displaystyle\\frac{1}{2}\\right)+0\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u653e\u7269\u7dda\u30682\u3064\u306e\u63a5\u7dda\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u9762\u7a4d<\/h3>\n<p>\u306a\u304a\u9762\u7a4d\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u5fae\u5206\u3092\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u50be\u304d\u3092\u8a08\u7b97\u3059\u308b\u30b1\u30fc\u30b9\u304c\u3072\u3093\u3071\u3093\u306b\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u7a4d\u5206\u3060\u3051\u3067\u306a\u304f\u3001\u5fae\u5206\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u5fae\u5206\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u30b1\u30fc\u30b9\u3068\u3057\u3066\u306f\u3001\u653e\u7269\u7dda\u3068\u63a5\u7dda\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u9762\u7a4d\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u305f\u5f8c\u3001\u653e\u7269\u7dda\u3068\u63a5\u7dda\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u305d\u308c\u305e\u308c\u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u89e3\u7b54\u3067\u304d\u307e\u3059\u3002<\/span>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u70b9\\((1,-3)\\)\u3092\u901a\u308b\\(y=x^2\\)\u306e\u63a5\u7dda\u306b\u3064\u3044\u3066\u3001\u63a5\u7dda\u3068\u653e\u7269\u7dda\u3067\u56f2\u307e\u308c\u308b\u90e8\u5206\u306e\u9762\u7a4d\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u50be\u304d\u3092\u5f97\u308b\u305f\u3081\u306b\u306f\u5fae\u5206\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\\(y=x^2\\)\u3092\u5fae\u5206\u3059\u308b\u3068\u3001\\(y&#8217;=2x\\)\u306b\u306a\u308a\u307e\u3059\u3002\u653e\u7269\u7dda\u4e0a\u306e\u63a5\u70b9\u3092\\((t,t^2)\\)\u3068\u3059\u308b\u3068\u3001\u63a5\u7dda\u306e\u50be\u304d\u306f\\(y&#8217;=2t\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(y-t^2=2t(x-t)\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\u63a5\u7dda\u306f\\((1,-3)\\)\u3092\u901a\u308b\u305f\u3081\u3001\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(-3-t^2=2t(1-t)\\)<\/p>\n<p>\\(t^2-2t-3=0\\)<\/p>\n<p>\\((t+1)(t-3)=0\\)<\/p>\n<p>\\(t=-1,3\\)<\/p>\n<p>\\(t=-1,3\\)\u3067\u3042\u308b\u305f\u3081\u3001\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e2\u3064\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(y=-2x-1\\)<\/li>\n<li>\\(y=6x-9\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fjeh5.jpg\" alt=\"\" width=\"428\" height=\"330\" class=\"aligncenter size-full wp-image-11609\" \/><\/p>\n<p>\u305d\u3053\u3067\u30012\u3064\u306e\u9762\u7a4d\u3092\u51fa\u3057\u3066\u8db3\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{1} \\{x^2-(-2x-1)\\} dx\\)\\(+\\displaystyle \\int_{1}^{3} \\{x^2-(6x-9)\\} dx\\)<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{1} (x^2+2x+1) dx\\)\\(+\\displaystyle \\int_{1}^{3} (x^2-6x+9) dx\\)<\/p>\n<p>\\(S=\\left[\\displaystyle\\frac{1}{3}x^3+x^2+x\\right]_{-1}^{1}\\)\\(+\\left[\\displaystyle\\frac{1}{3}x^3-3x^2+9x\\right]_{1}^{3}\\)<\/p>\n<p>\\(S=\\left(\\displaystyle\\frac{1}{3}+1+1\\right)\\)\\(-\\left(-\\displaystyle\\frac{1}{3}+1-1\\right)\\)\\(+(9-27+27)\\)\\(-\\left(\\displaystyle\\frac{1}{3}-3+9\\right)\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{16}{3}\\)<\/p>\n<p>\u5fae\u5206\u3092\u5229\u7528\u3057\u3066\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u9762\u7a4d\u3092\u5f97\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u7d76\u5bfe\u5024\u3092\u542b\u3080\u7a4d\u5206\u306e\u8a08\u7b97<\/h2>\n<p>\u8a08\u7b97\u554f\u984c\u306b\u3088\u3063\u3066\u306f\u3001\u7d76\u5bfe\u5024\u3092\u542b\u3080\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u7d76\u5bfe\u5024\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u3001\u7b54\u3048\u306f\u5fc5\u305a\u30d7\u30e9\u30b9\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u7d76\u5bfe\u5024\u306e\u4e2d\u304c\u30de\u30a4\u30ca\u30b9\u306e\u5834\u5408\u3001\u30d7\u30e9\u30b9\u306b\u3059\u308b\u305f\u3081\u3001\u30de\u30a4\u30ca\u30b9\u3092\u52a0\u3048\u3066\u7d76\u5bfe\u5024\u3092\u5916\u3055\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u3053\u3067\u7d76\u5bfe\u5024\u306e\u4e2d\u304c\u30d7\u30e9\u30b9\u306b\u306a\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u306e\u304b\u78ba\u8a8d\u3057\u3066\u7d76\u5bfe\u5024\u3092\u5916\u3057\u3001\u305d\u308c\u305e\u308c\u7a4d\u5206\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{-2}^{1} |x^2-x| dx\\)<\/li>\n<\/ul>\n<p>\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/jdhw2.jpg\" alt=\"\" width=\"397\" height=\"261\" class=\"aligncenter size-full wp-image-11616\" \/><\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\int_{-2}^{0} (x^2-x) dx\\)\\(+\\displaystyle \\int_{0}^{1} (-x^2+x) dx\\)<\/p>\n<p>\\(=\\left[\\displaystyle\\frac{1}{3}x^3-\\displaystyle\\frac{1}{2}x^2\\right]_{-2}^{0}\\)\\(+\\left[-\\displaystyle\\frac{1}{3}x^3+\\displaystyle\\frac{1}{2}x^2\\right]_{0}^{1}\\)<\/p>\n<p>\\(=0-\\left(-\\displaystyle\\frac{8}{3}-2\\right)\\)\\(+\\left(-\\displaystyle\\frac{1}{3}+\\displaystyle\\frac{1}{2}\\right)-0\\)<\/p>\n<p>\\(=\\displaystyle\\frac{29}{6}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7d76\u5bfe\u5024\u3092\u542b\u3080\u8a08\u7b97\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u306a\u304a\u3001<span style=\"color: #0000ff;\">\u7d76\u5bfe\u5024\u3092\u542b\u3080\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3068\u3044\u3046\u306e\u306f\u3001\u95a2\u6570\u3068\\(x\\)\u8ef8\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u9762\u7a4d\u306e\u8a08\u7b97\u3068\u5f0f\u304c\u540c\u3058\u3067\u3059\u3002<\/span>\u305d\u306e\u305f\u3081\\(\\displaystyle \\int_{-2}^{1} |x^2-x| dx\\)\u3068\u3044\u3046\u306e\u306f\u3001\\(-2\u2266x\u22661\\)\u306e\u7bc4\u56f2\u306b\u3064\u3044\u3066\\(y=x^2-x\\)\u3068\\(x\\)\u8ef8\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u9762\u7a4d\u306e\u8a08\u7b97\u3068\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u5b9a\u7a4d\u5206\u306b\u3088\u308b\u9762\u7a4d\u306e\u8a08\u7b97\u3092\u5b66\u3079\u3070\u3001\u7d76\u5bfe\u5024\u3092\u542b\u3080\u5834\u5408\u306e\u8a08\u7b97\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h2>2\u3064\u306e\u4ea4\u70b9\u3067\u5229\u7528\u3067\u304d\u308b6\u5206\u306e1\u516c\u5f0f<\/h2>\n<p>\u306a\u304a\u5b9a\u7a4d\u5206\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u30016\u5206\u306e1\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u516c\u5f0f\u3092\u77e5\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u8a08\u7b97\u30b9\u30d4\u30fc\u30c9\u304c\u901f\u304f\u306a\u308a\u307e\u3059\u30022\u3064\u306e\u63a5\u70b9\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u30016\u5206\u306e1\u516c\u5f0f\u304c\u5f79\u7acb\u3061\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u30b1\u30fc\u30b9\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u76f4\u7dda\u3068\u653e\u7269\u7dda\u306b\u3088\u308b\u9762\u7a4d<\/li>\n<li>\u653e\u7269\u7dda\u3068\u653e\u7269\u7dda\u306b\u3088\u308b\u9762\u7a4d<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/jdhw3.jpg\" alt=\"\" width=\"600\" height=\"241\" class=\"aligncenter size-full wp-image-11618\" \/><\/p>\n<p>2\u3064\u306e\u65b9\u7a0b\u5f0f\u304c\u4ea4\u70b9\u3092\u3082\u3064\u5834\u5408\u3001\u9023\u7acb\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u3063\u3066\\(x\\)\u8ef8\u306e\u4ea4\u70b9\u5ea7\u6a19\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\\(x\\)\u8ef8\u306e\u4ea4\u70b9\u5ea7\u6a19\u3092\\(\u03b1\\)\u3001\\(\u03b2\\)\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\((x-\u03b1)(x-\u03b2)=0\\)<\/li>\n<\/ul>\n<p>2\u3064\u306e\u65b9\u7a0b\u5f0f\u306e\u4ea4\u70b9\uff08\u9023\u7acb\u3055\u305b\u305f\u5f0f\uff09\u306b\u3064\u3044\u3066\u3001\\(x\\)\u306e\u7b54\u3048\u304c\\(\u03b1\\)\u3001\\(\u03b2\\)\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u5f0f\u3092\u4f5c\u308c\u308b\u306e\u306f\u554f\u984c\u306a\u304f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u4ea4\u70b9\u3068\u5b9a\u7a4d\u5206\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u30b0\u30e9\u30d5\u306e\u4e0a\u306b\u3042\u308b\u5f0f\u304b\u3089\u30b0\u30e9\u30d5\u306e\u4e0b\u306b\u3042\u308b\u5f0f\u3092\u5f15\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3064\u307e\u308a\u3001\u9023\u7acb\u3055\u305b\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\\(y=(x-\u03b1)(x-\u03b2)\\)\u306e\u5f0f\u3092\u4f5c\u308c\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u304c6\u5206\u306e1\u516c\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{\u03b1}^{\u03b2} (x-\u03b1)(x-\u03b2) dx=-\\displaystyle\\frac{1}{6}(\u03b2-\u03b1)^3\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff08\u8a3c\u660e\u65b9\u6cd5\u3092\u899a\u3048\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\uff09\u3002<\/p>\n<p>\\(\\displaystyle \\int_{\u03b1}^{\u03b2} (x-\u03b1)(x-\u03b2) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int_{\u03b1}^{\u03b2} (x-\u03b1)\\{(x-\u03b1)-(\u03b2-\u03b1)\\} dx\\)<\/p>\n<p>\\(=\\displaystyle \\int_{\u03b1}^{\u03b2} \\{(x-\u03b1)^2-(\u03b2-\u03b1)(x-\u03b1)\\} dx\\)<\/p>\n<p>\\(=\\left[\\displaystyle\\frac{1}{3}(x-\u03b1)^3-(\u03b2-\u03b1)\u00b7\\displaystyle\\frac{1}{2}(x-\u03b1)^2\\right]_{\u03b1}^{\u03b2}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{3}(\u03b2-\u03b1)^3-\\displaystyle\\frac{1}{2}(\u03b2-\u03b1)^3\\)<\/p>\n<p>\\(=-\\displaystyle\\frac{1}{6}(\u03b2-\u03b1)^3\\)<\/p>\n<p>\u203b\u3053\u306e\u8a08\u7b97\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u304b\u3063\u3053\u5185\u306b\u5909\u6570\u3092\u542b\u3080\u5834\u5408\u306e\u7a4d\u5206\u3092\u77e5\u3063\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5b9f\u969b\u306b6\u5206\u306e1\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u305f\u3002<\/p>\n<ul>\n<li>\\(y=x^2\\)\u3068\\(y=-x^2-x+1\\)\u306b\u3088\u3063\u3066\u56f2\u307e\u308c\u308b\u9762\u7a4d\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5148\u307b\u3069\u306e\u8a08\u7b97\u3088\u308a\u30012\u66f2\u7dda\u306e\\(x\\)\u8ef8\u306e\u4ea4\u70b9\u306f\\(x=-1,\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/fjeh3.jpg\" alt=\"\" width=\"519\" height=\"308\" class=\"aligncenter size-full wp-image-11606\" \/><\/p>\n<p>\u305d\u3053\u30676\u5206\u306e1\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{\\frac{1}{2}} \\{(-x^2-x+1)-(x^2)\\} dx\\)<\/p>\n<p>\\(S=\\displaystyle \\int_{-1}^{\\frac{1}{2}} (-2x^2-x+1) dx\\)<\/p>\n<p>\\(S=-\\displaystyle \\int_{-1}^{\\frac{1}{2}} (2x^2+x-1) dx\\)<\/p>\n<p>\\(S=-\\displaystyle \\int_{-1}^{\\frac{1}{2}} (x+1)(2x-1) dx\\)<\/p>\n<p>\\(S=-2\\displaystyle \\int_{-1}^{\\frac{1}{2}} (x+1)(x-\\displaystyle\\frac{1}{2}) dx\\)<\/p>\n<p>\\(S=2\u00d7\\displaystyle\\frac{1}{6}\\left(\\displaystyle\\frac{1}{2}+1\\right)^3\\)<\/p>\n<p>\\(S=2\u00d7\\displaystyle\\frac{1}{6}\u00d7\\displaystyle\\frac{27}{8}\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{9}{8}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5148\u307b\u3069\u3068\u540c\u3058\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u6ce8\u610f\u70b9\u3068\u3057\u3066\u30016\u5206\u306e1\u516c\u5f0f\u306f\u7a4d\u5206\u8a18\u53f7\u5185\u306b\u3042\u308b\\(x\\)\u306e\u4fc2\u6570\u304c1\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\\(-\\displaystyle \\int_{-1}^{\\frac{1}{2}} (x+1)(2x-1) dx\\)\u3092\\(-2\\displaystyle \\int_{-1}^{\\frac{1}{2}} (x+1)(x-\\displaystyle\\frac{1}{2}) dx\\)\u3078\u5909\u63db\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5b9a\u7a4d\u5206\u306b\u3088\u308b\u9762\u7a4d\u306e\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024<\/h3>\n<p>\u5b9a\u7a4d\u5206\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u5909\u6570\u304c\u542b\u307e\u308c\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u9762\u7a4d\u304c\u5909\u5316\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u9762\u7a4d\u306e\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5b9a\u7a4d\u5206\u3092\u3057\u305f\u5f8c\u3001\u5f0f\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u3067\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3068\u306a\u308b\u5024\u3092\u5f97\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u70b9\\((1,2)\\)\u3092\u901a\u308b\u76f4\u7dda\u3068\u653e\u7269\u7dda\\(y=x^2\\)\u304c2\u70b9\u3067\u4ea4\u308f\u308b\u3068\u304d\u3001\u76f4\u7dda\u3068\u653e\u7269\u7dda\u3067\u56f2\u307e\u308c\u308b\u9762\u7a4d\\(S\\)\u306e\u6700\u5c0f\u5024\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u70b9\\((1,2)\\)\u3092\u901a\u308b\u76f4\u7dda\u306e\u50be\u304d\u3092\\(m\\)\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(y-2=m(x-1)\\)<\/p>\n<p>\\(y=mx-m+2\\)<\/p>\n<p>\\(y=mx-m+2\\)\u3068\\(y=x^2\\)\u306e\u4ea4\u70b9\u306b\u3064\u3044\u3066\u3001\\(x\\)\u5ea7\u6a19\u306f\u308f\u304b\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u4ea4\u70b9\u306e\\(x\\)\u5ea7\u6a19\u3092\\(\u03b1\\)\u3068\\(\u03b2\\)\u306b\u3057\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/jdhw1-1.jpg\" alt=\"\" width=\"501\" height=\"259\" class=\"aligncenter size-full wp-image-11615\" \/><\/p>\n<p>\u307e\u305f\u3001\u30b0\u30e9\u30d5\u306e\u4e0a\u306b\u3042\u308b\u95a2\u6570\u304b\u3089\u30b0\u30e9\u30d5\u306e\u4e0b\u306b\u3042\u308b\u95a2\u6570\u3092\u5f15\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5b9a\u7a4d\u5206\u3067\u5229\u7528\u3059\u308b\u95a2\u6570\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(mx-m+2-(x^2)\\)<\/p>\n<p>\\(=-x^2+mx-m+2\\)<\/p>\n<p>\u307e\u305f\u76f4\u7dda\u3068\u653e\u7269\u7dda\u306b\u3088\u308b2\u3064\u306e\u63a5\u70b9\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u30016\u5206\u306e1\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4ea4\u70b9\u306e\\(x\\)\u5ea7\u6a19\u306f\\(\u03b1\\)\u3068\\(\u03b2\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7a4d\u5206\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(S=\\displaystyle \\int_{\u03b1}^{\u03b2} (-x^2+mx-m+2) dx\\)<\/p>\n<p>\\(S=-\\displaystyle \\int_{\u03b1}^{\u03b2} (x^2-mx+m-2) dx\\)<\/p>\n<p>\\(S=-\\displaystyle \\int_{\u03b1}^{\u03b2} (x-\u03b1)(x-\u03b2) dx\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{1}{6}(\u03b2-\u03b1)^3\\)<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\\(\u03b2-\u03b1\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\\(x^2-mx+m-2=0\\)\u306b\u3064\u3044\u3066\u3001\u5224\u5225\u5f0f\u3092\\(D\\)\u3068\u3059\u308b\u3068\u3001\u89e3\u306e\u516c\u5f0f\u3088\u308a\u7b54\u3048\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x=\\displaystyle\\frac{m\u00b1\\sqrt{D}}{2}\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(\u03b2-\u03b1\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\u03b2-\u03b1=\\displaystyle\\frac{m+\\sqrt{D}}{2}-\\displaystyle\\frac{m-\\sqrt{D}}{2}\\)<\/p>\n<p>\\(\u03b2-\u03b1=\\sqrt{D}\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\u5224\u5225\u5f0f\\(D\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(D=m^2-4(m-2)\\)<\/p>\n<p>\\(D=m^2-4m+8\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\\(\u03b2-\u03b1=\\sqrt{m^2-4m+8}\\)\u3067\u3059\u3002\u3053\u306e\u7d50\u679c\u304b\u3089\u3001\u3069\u306e\u3088\u3046\u306b\u6700\u5c0f\u5024\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002\\(S=\\displaystyle\\frac{1}{6}(\u03b2-\u03b1)^3\\)\u304c\u6700\u5c0f\u306b\u306a\u308b\u305f\u3081\u306b\u306f\u3001\\(\u03b2-\u03b1\\)\u304c\u6700\u5c0f\u306b\u306a\u308c\u3070\u3044\u3044\u3067\u3059\u3002<\/p>\n<p>\u4e8c\u6b21\u95a2\u6570\u3067\u6700\u5c0f\u5024\u3092\u5f97\u308b\u305f\u3081\u306b\u306f\u3001\u4e8c\u4e57\u3092\u4f5c\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\u03b2-\u03b1=\\sqrt{m^2-4m+8}\\)<\/p>\n<p>\\(\u03b2-\u03b1=\\sqrt{(m-2)^2+4}\\)<\/p>\n<p>\u3064\u307e\u308a\u3001\\(m=2\\)\u306e\u3068\u304d\\(\u03b2-\u03b1=2\\)\u3068\u306a\u308a\u3001\u9762\u7a4d\u306f\u6700\u5c0f\u5024\u3068\u306a\u308a\u307e\u3059\u3002\u307e\u305f\\(\u03b2-\u03b1=2\\)\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001\\(S=\\displaystyle\\frac{4}{3}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u5b9a\u7a4d\u5206\u30686\u5206\u306e1\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u306e\u6700\u5c0f\u5024\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u7a4d\u5206\u3092\u5229\u7528\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u79c1\u305f\u3061\u304c\u6570\u5b66\u3067\u7a4d\u5206\u3092\u5b66\u3076\u306e\u306f\u3001\u9762\u7a4d\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u305f\u3081\u3067\u3059\u3002\u7279\u306b\u529b\u5b66\u3084\u571f\u6728\u3001\u822a\u7a7a\u5b87\u5b99\u3001\u91cf\u5b50\u529b\u5b66\u306a\u3069\u3001\u7269\u7406\u3067\u306f\u7a4d\u5206\u304c\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5b9a\u7a4d\u5206\u3092\u3059\u308b\u3068\u304d\u3001\\(y\\)\u306e\u5024\u304c\u30d7\u30e9\u30b9\u306a\u306e\u304b\u30de\u30a4\u30ca\u30b9\u306a\u306e\u304b\u306b\u3088\u3063\u3066\u3001\u30de\u30a4\u30ca\u30b9\u3092\u52a0\u3048\u3066\u5b9a\u7a4d\u5206\u3092\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u306e\u304b\u3069\u3046\u304b\u304c\u5909\u308f\u308a\u307e\u3059\u3002\u307e\u305f\u4e8c\u3064\u306e\u7dda\u3092\u7528\u3044\u3066\u7a4d\u5206\u3092\u3059\u308b\u5834\u5408\u3001\u3069\u3061\u3089\u304c\u30b0\u30e9\u30d5\u306e\u4e0a\u5074\u306b\u306a\u308b\u306e\u304b\u78ba\u8a8d\u3057\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u3068\u304d\u30016\u5206\u306e1\u516c\u5f0f\u3092\u899a\u3048\u3066\u3044\u308b\u3068\u8a08\u7b97\u304c\u901f\u3044\u3067\u3059\u3002<\/p>\n<p>\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u7d76\u5bfe\u5024\u3092\u542b\u3080\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u304c\u51fa\u984c\u3055\u308c\u307e\u3059\u3002\u305f\u3060\u7d76\u5bfe\u5024\u3092\u542b\u3080\u5834\u5408\u306e\u8a08\u7b97\u3068\u3044\u3046\u306e\u306f\u3001\u66f2\u7dda\u3068\\(x\\)\u8ef8\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u9762\u7a4d\u306e\u8a08\u7b97\u3068\u8003\u3048\u65b9\u304c\u540c\u3058\u3067\u3059\u3002<\/p>\n<p>\u9762\u7a4d\u306e\u8a08\u7b97\u3067\u306f\u3001\u5fdc\u7528\u554f\u984c\u3082\u3072\u3093\u3071\u3093\u306b\u51fa\u3055\u308c\u307e\u3059\u3002\u305d\u306e\u4e2d\u3067\u3082\u9762\u7a4d\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u306f\u6700\u3082\u4e00\u822c\u7684\u306a\u554f\u984c\u3067\u3042\u308b\u305f\u3081\u3001\u89e3\u3051\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u6570\u5b66\u3067\u7a4d\u5206\u306f\u91cd\u8981\u306a\u5206\u91ce\u3067\u3042\u308b\u305f\u3081\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u7406\u89e3\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n","prote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\\(x\\)\u8ef8\u3068\u66f2\u7dda\u306b\u3088\u308b\u9762\u7a4d\u3092\u8a08\u7b97\u3057\u305f\u3044\u5834\u5408\u3001\\(y\\)\u8ef8\u306e\u5024\u304c\u30d7\u30e9\u30b9\u306b\u306a\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u306e\u304b\u306b\u3088\u3063\u3066\u7b26 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11624,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-11586","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-h-math"},"_links":{"self":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11586","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/comments?post=11586"}],"version-history":[{"count":15,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11586\/revisions"}],"predecessor-version":[{"id":11693,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11586\/revisions\/11693"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/11624"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=11586"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=11586"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=11586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}