{"id":11552,"date":"2022-12-12T02:09:51","date_gmt":"2022-12-11T17:09:51","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11552"},"modified":"2022-12-17T09:57:40","modified_gmt":"2022-12-17T00:57:40","slug":"integral","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/integral.html","title":{"rendered":"\u4e0d\u5b9a\u7a4d\u5206\u30fb\u5b9a\u7a4d\u5206\uff1a\u516c\u5f0f\u3084\u8a08\u7b97\u65b9\u6cd5\u3001\u5fae\u5206\u3068\u306e\u95a2\u4fc2"},"content":{"rendered":"\n<p>\u5fae\u5206\u306e\u53cd\u5bfe\u304c\u7a4d\u5206\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u7a4d\u5206\u3092\u5b66\u3076\u3068\u304d\u3001\u4e8b\u524d\u306b\u5fae\u5206\u3092\u7406\u89e3\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u5fae\u5206\u306e\u53cd\u5bfe\u3092\u516c\u5f0f\u3068\u3057\u3066\u899a\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7a4d\u5206\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u3001\u7279\u5b9a\u306e\u7bc4\u56f2\u3092\u6307\u5b9a\u305b\u305a\u306b\u7a4d\u5206\u3092\u3059\u308b\u5834\u5408\u3001\u4e0d\u5b9a\u7a4d\u5206\u3092\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3067\u7279\u5b9a\u306e\u7bc4\u56f2\u306b\u3064\u3044\u3066\u9762\u7a4d\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u3001\u5b9a\u7a4d\u5206\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u7a4d\u5206\u306b\u3088\u3063\u3066\u3001\u9762\u7a4d\u3092\u5f97\u308b\u305f\u3081\u306e\u95a2\u6570\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5177\u4f53\u7684\u306a\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u5b9a\u7a4d\u5206\u3092\u5229\u7528\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d\u3001\u4e0d\u5b9a\u7a4d\u5206\u3084\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\u3092\u899a\u3048\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u7a4d\u5206\u540c\u58eb\u3067\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u5b66\u3076\u306e\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u7a4d\u5206\u306e\u516c\u5f0f\u306b\u306f\u4f55\u304c\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u307e\u305f\u3001\u3069\u306e\u3088\u3046\u306b\u7a4d\u5206\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u7a4d\u5206\u3092\u884c\u3046\u57fa\u672c\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u5fae\u5206\u306e\u9006\u306b\u3088\u308a\u3001\u4e0d\u5b9a\u7a4d\u5206\u3092\u884c\u3046\uff1a\u4e0d\u5b9a\u7a4d\u5206\u306e\u516c\u5f0f<\/h2>\n<p>\u9762\u7a4d\u3092\u5f97\u308b\u95a2\u6570\u3092\u5f97\u305f\u3044\u3068\u304d\u3001\u7a4d\u5206\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u5fae\u5206\u3068\u7a4d\u5206\u306f\u89aa\u305b\u304d\u306e\u95a2\u4fc2\u306b\u3042\u308a\u3001\u5fae\u5206\u306e\u53cd\u5bfe\u304c\u7a4d\u5206\u306b\u8a72\u5f53\u3057\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/ewt3.jpg\" alt=\"\" width=\"600\" height=\"94\" class=\"aligncenter size-full wp-image-5171\" \/><\/p>\n<p>\u4f8b\u3048\u3070\\(f(x)=x^n\\)\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f'(x)=nx^{n-1}\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067<span style=\"color: #0000ff;\">\u7a4d\u5206\u3067\u306f\u3001\u3053\u306e\u53cd\u5bfe\u3092\u516c\u5f0f\u306b\u3059\u308c\u3070\u3044\u3044\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/span>\u4f8b\u3048\u3070\\(f(x)=x^n\\)\u3092\u7a4d\u5206\u3059\u308b\u3068\u304d\u3001\u516c\u5f0f\u306f\u4ee5\u4e0b\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int f(x) dx=\\displaystyle\\frac{1}{n+1}x^{n+1}+C\\)<\/li>\n<\/ul>\n<p>\u53c2\u8003\u307e\u3067\u306b\u3001\\(\\displaystyle\\frac{1}{n+1}x^{n+1}+C\\)\u3092\u5fae\u5206\u3059\u308b\u3068\\(x^n\\)\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u7a4d\u5206\u306e\u516c\u5f0f\u3092\u6697\u8a18\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u5fae\u5206\u3068\u7a4d\u5206\u306e\u95a2\u4fc2\u3092\u5b66\u3076\u3053\u3068\u3067\u516c\u5f0f\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u7a4d\u5206\u306e\u516c\u5f0f\u3067\\(+C\\)\u304c\u5b58\u5728\u3059\u308b\u306e\u306f\u3001\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u30660\u306b\u306a\u308b\u304b\u3089\u3067\u3059\u3002\u5177\u4f53\u7684\u306b\u3069\u306e\u3088\u3046\u306a\u5024\u304c\\(C\\)\u306b\u8a72\u5f53\u3059\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u3001\u7a4d\u5206\u3060\u3051\u3067\u306f\u5224\u65ad\u3067\u304d\u307e\u305b\u3093\u3002\\(C\\)\u306e\u5024\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u3001\u307b\u304b\u306e\u6761\u4ef6\u3068\u6bd4\u8f03\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3>\u4e0d\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\uff1a\u5b9a\u6570\u500d\u3068\u8db3\u3057\u7b97\u30fb\u5f15\u304d\u7b97\u306e\u30eb\u30fc\u30eb<\/h3>\n<p>\u306a\u304a\u95a2\u6570\\(F(x)\\)\u3092\u5fae\u5206\u3059\u308b\u3053\u3068\u3067\u95a2\u6570\\(f(x)\\)\u3092\u5f97\u3089\u308c\u308b\u3068\u3057\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u95a2\u6570\\(f(x)\\)\u3092\u7a4d\u5206\u3059\u308b\u3068\u95a2\u6570\\(F(x)\\)\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001<span style=\"color: #ff0000;\">\u95a2\u6570\\(F(x)\\)\u306f\\(f(x)\\)\u306e\u4e0d\u5b9a\u7a4d\u5206\u3067\u3059\u3002<\/span><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5b9f\u969b\u306b\u7a4d\u5206\u3092\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4e0d\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\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 (x-2)(x-3) dx\\)<\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\int (x-2)(x-3) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int (x^2-5x+6) dx\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{3}x^3-\\displaystyle\\frac{5}{2}x^2+6x+C\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7a4d\u5206\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p><strong>\u30fb\u5b9a\u6570\u500d\u3059\u308b\u3068\u304d\u3001\u6570\u5b57\u3092\u7a4d\u5206\u8a18\u53f7\u306e\u4e2d\u3092\u5165\u308c\u3089\u308c\u308b\uff08\u307e\u305f\u306f\u5916\u3078\u51fa\u305b\u308b\uff09<\/strong><\/p>\n<p>\u306a\u304a\u304b\u3051\u7b97\u3084\u5272\u308a\u7b97\uff08\u5206\u6570\u306e\u304b\u3051\u7b97\uff09\u3092\u5f0f\u306b\u542b\u3080\u5834\u5408\u3001\u7a4d\u5206\u8a18\u53f7\u306e\u4e2d\u3078\u6570\u5b57\u3092\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(2\\displaystyle \\int (x-2)(x-3) dx\\)<\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\(2\\displaystyle \\int (x-2)(x-3) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int 2(x-2)(x-3) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int 2(x^2-5x+6) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int (2x^2-10x+12) dx\\)<\/p>\n<p>\\(=\\displaystyle\\frac{2}{3}x^3-5x^2+12x+C\\)<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u306a\u304a\u3001\u4e0d\u5b9a\u7a4d\u5206\u306e\u5b9a\u6570\u500d\u3092\u6570\u5f0f\u3067\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(k\\displaystyle \\int f(x) dx=\\displaystyle \\int k\u00b7f(x) dx\\)<\/li>\n<\/ul>\n<p>\u5b9a\u6570\u500d\u306b\u95a2\u3059\u308b\u7a4d\u5206\u3067\u306f\u3001\u7a4d\u5206\u8a18\u53f7\u306e\u4e2d\u306b\u6570\u5b57\u3092\u5165\u308c\u305f\u308a\u3001\u53cd\u5bfe\u306b\u6570\u5b57\u3092\u7a4d\u5206\u8a18\u53f7\u306e\u5916\u306b\u51fa\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3067\u306f\u3001\u4e0d\u5b9a\u7a4d\u5206\u3092\u5408\u4f53\u3067\u304d\u308b<\/strong><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4e0d\u5b9a\u7a4d\u5206\u306e\u8db3\u3057\u7b97\u30fb\u5f15\u304d\u7b97\u306f\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3092\u3059\u308b\u5834\u5408\u3001\u7a4d\u5206\u8a18\u53f7\u3092\u4ed8\u3051\u305f\u307e\u307e\u95a2\u6570\u540c\u58eb\u306e\u8db3\u3057\u7b97\u30fb\u5f15\u304d\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int (x+2) dx+\\displaystyle \\int (x+4) dx\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u5f0f\u306b\u3064\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\\(x+2\\)\u3068\\(x+4\\)\u3092\u8db3\u3057\u3001\u305d\u306e\u3042\u3068\u306b\u7a4d\u5206\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\int (x+2) dx+\\displaystyle \\int (x+4) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int (x+2+x+4) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int (2x+6) dx\\)<\/p>\n<p>\\(=x^2+6x+C\\)<\/p>\n<p>\u95a2\u6570\u540c\u58eb\u306e\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u8a08\u7b97\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u306a\u304a\u3001\u6570\u5f0f\u3067\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int f(x) dx+\\displaystyle \\int g(x) dx\\)\\(=\\displaystyle \\int \\{f(x)+g(x)\\} dx\\)<\/li>\n<li>\\(m\\displaystyle \\int f(x) dx+n\\displaystyle \\int g(x) dx\\)\\(=\\displaystyle \\int \\{m\u00b7f(x)+n\u00b7g(x)\\} dx\\)<\/li>\n<\/ul>\n<p>\u516c\u5f0f\u3092\u899a\u3048\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u7279\u5b9a\u306e\u7bc4\u56f2\u3092\u8a08\u7b97\u3059\u308b\u5b9a\u7a4d\u5206<\/h2>\n<p>\u306a\u304a\u4e0d\u5b9a\u7a4d\u5206\u3068\u3057\u3066\u95a2\u6570\u3092\u5f97\u305f\u3068\u3057\u3066\u3082\u3001\u9762\u7a4d\u3092\u5f97\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u7bc4\u56f2\u3092\u6c7a\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\\(f(x)=2x\\)\u306b\u3064\u3044\u3066\u3001\u7a4d\u5206\u3092\u3059\u308b\u3068\\(F(x)=x^2\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305f\u3060\u4e0d\u5b9a\u7a4d\u5206\\(F(x)=x^2\\)\u306b\u3064\u3044\u3066\u3001\\(x\\)\u306e\u7bc4\u56f2\u304c\\(0\u2266x\u22661\\)\u306e\u5834\u5408\u3068\\(0\u2266x\u22662\\)\u306e\u5834\u5408\u3092\u6bd4\u3079\u308b\u3068\u3001\u5f97\u3089\u308c\u308b\u7b54\u3048\uff08\u9762\u7a4d\uff09\u306f\u7570\u306a\u308b\u3068\u5bb9\u6613\u306b\u7406\u89e3\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u7bc4\u56f2\u3092\u6307\u5b9a\u3059\u308b\u306e\u3067\u3059\u3002\u4f8b\u3048\u3070\u4ee5\u4e0b\u306e\u5f0f\u3068\u3044\u3046\u306e\u306f\u3001\u95a2\u6570\\(f(x)=2x\\)\u3092\u7a4d\u5206\u3057\u3001\\(0\u2266x\u22661\\)\u3067\u306e\u9762\u7a4d\u3092\u6c42\u3081\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{0}^{1} (2x) dx\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/dhw4.jpg\" alt=\"\" width=\"363\" height=\"296\" class=\"aligncenter size-full wp-image-11566\" \/><\/p>\n<p>\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3067\u306f\u3001\\(f(x)\\)\u306b\u5bfe\u3057\u3066\u7a4d\u5206\u3092\u3057\u305f\u5f8c\u3001\\(x\\)\u306e\u7bc4\u56f2\u3092\u7528\u3044\u3066\u5f15\u304d\u7b97\u3092\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\\(f(x)\\)\u3092\u7a4d\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\\(F(x)\\)\u3092\u5f97\u305f\u3068\u3057\u307e\u3059\u3002\\(x\\)\u306e\u7bc4\u56f2\u304c\\(0\u2266x\u22661\\)\u306a\u306e\u3067\u3042\u308c\u3070\u3001\\(F(1)\\)\u304b\u3089\\(F(0)\\)\u3092\u5f15\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u9762\u7a4d\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u5148\u307b\u3069\u306e\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3057\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle \\int_{0}^{1} (2x) dx=\\left[x^2\\right]_0^1\\)<\/p>\n<p>\u304b\u3063\u3053\u306e\u4e2d\u306b\u7a4d\u5206\u5f8c\u306e\u7d50\u679c\u3092\u8a18\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u304b\u3063\u3053\u306e\u53f3\u306b\u7bc4\u56f2\u3092\u8a18\u8f09\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u306e\u5f8c\u3001\u7a4d\u5206\u5f8c\u306e\u95a2\u6570\u306b\u5024\u3092\u4ee3\u5165\u3059\u308b\u3053\u3068\u3067\u5f15\u304d\u7b97\u3092\u3057\u307e\u3059\u3002\u5148\u307b\u3069\u306e\u5f0f\uff08\u7a4d\u5206\u5f8c\u306e\u5f0f\uff09\u306b\u5024\u3092\u4ee3\u5165\u3057\u3001\\(F(1)\\)\u304b\u3089\\(F(0)\\)\u3092\u5f15\u304f\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\left[x^2\\right]_0^1\\)<\/p>\n<p>\\(=1-0\\)<\/p>\n<p>\\(=1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\\(y=2x\\)\u306b\u3064\u3044\u3066\u3001\\(x\\)\u306e\u7bc4\u56f2\u304c\\(0\u2266x\u22661\\)\u306e\u5834\u5408\u3001\u9762\u7a4d\u306f1\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u306a\u304a\u56f3\u3092\u78ba\u8a8d\u3059\u308b\u3068\u3001\u305f\u3066\u306e\u9577\u3055\u304c2\u3001\u6a2a\u306e\u9577\u3055\u304c1\u306e\u76f4\u89d2\u4e09\u89d2\u5f62\u3067\u3042\u308b\u305f\u3081\u3001\u7a4d\u5206\u3092\u3057\u306a\u304f\u3066\u3082\u7b54\u3048\u306f1\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u7a4d\u5206\u3092\u3059\u308b\u5834\u5408\u3068\u7b54\u3048\u304c\u4e00\u81f4\u3059\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u3053\u3053\u307e\u3067\u306e\u8a08\u7b97\u3092\u4e00\u822c\u5316\u3057\u307e\u3057\u3087\u3046\u3002\u95a2\u6570\\(f(x)\\)\u3092\u7a4d\u5206\u3059\u308b\u3053\u3068\u3067\\(F(x)\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5b9a\u7a4d\u5206\u306e\u7bc4\u56f2\u304c\\(a\\)\u304b\u3089\\(b\\)\u307e\u3067\u306e\u5834\u5408\u3001\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{a}^{b} f(x) dx\\)\\(=\\left[F(x)\\right]_a^b\\)\\(=F(b)-F(a)\\)<\/li>\n<\/ul>\n<p>\u77e5\u8b58\u306a\u3057\u306b\u516c\u5f0f\u3092\u898b\u3066\u3082\u7406\u89e3\u3057\u306b\u304f\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u5177\u4f53\u4f8b\u3092\u78ba\u8a8d\u3057\u305f\u5f8c\u306b\u516c\u5f0f\u306e\u610f\u5473\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3067\u306f\u3001\u7a4d\u5206\u8a08\u7b97\u3059\u308b\u3068\u304d\u306b\\(+C\\)\u3092\u7701\u7565\u3057\u307e\u3059\u3002\u7406\u7531\u3068\u3057\u3066\u306f\u3001\u5f15\u304d\u7b97\u3092\u3059\u308b\u3068\u304d\u306b\u6d88\u53bb\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002\u4f8b\u3068\u3057\u3066\u3001\\(\\displaystyle \\int_{0}^{1} (2x) dx\\)\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\int_{0}^{1} (2x) dx\\)<\/p>\n<p>\\(\\left[x^2+C\\right]_0^1\\)<\/p>\n<p>\\(=(1+C)-(0+C)\\)<\/p>\n<p>\\(=1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5148\u307b\u3069\u3068\u540c\u3058\u7b54\u3048\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u304c\u3001\u5b9a\u7a4d\u5206\u3067\\(+C\\)\u3092\u7701\u7565\u3067\u304d\u308b\u7406\u7531\u3067\u3059\u3002<\/p>\n<h3>\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\u3068\u8a08\u7b97\u65b9\u6cd5<\/h3>\n<p>\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\u306f\u4e0d\u5b9a\u7a4d\u5206\u3068\u540c\u3058\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u5b9a\u6570\u500d\u3092\u3059\u308b\u3068\u304d\u3001\u7a4d\u5206\u8a18\u53f7\u306e\u4e2d\u306b\u6570\u5b57\u3092\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(k\\displaystyle \\int_{a}^{b} f(x) dx\\)\\(=\\displaystyle \\int_{a}^{b} k\u00b7f(x) dx\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u7bc4\u56f2\u304c\u540c\u3058\u5834\u5408\u3001\u8db3\u3057\u7b97\u3084\u5f15\u304d\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{a}^{b} f(x) dx+\\displaystyle \\int_{a}^{b} g(x) dx\\)\\(=\\displaystyle \\int_{a}^{b} \\{f(x)+g(x)\\} dx\\)<\/li>\n<li>\\(m\\displaystyle \\int_{a}^{b} f(x) dx+n\\displaystyle \\int_{a}^{b} g(x) dx\\)\\(=\\displaystyle \\int_{a}^{b} \\{m\u00b7f(x)+n\u00b7g(x)\\} dx\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u5b9a\u7a4d\u5206\u306b\u7279\u6709\u306e\u6027\u8cea\u306b\u306f\u4f55\u304c\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7bc4\u56f2\u304c0\u306e\u5834\u5408\u3001\u9762\u7a4d\u306f0\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{a}^{a} f(x) dx=0\\)<\/li>\n<\/ul>\n<p>\u7bc4\u56f2\u304c\\(a\\)\u304b\u3089\\(a\\)\u3067\u3042\u308b\u305f\u3081\u3001\u7b54\u3048\uff08\u9762\u7a4d\uff09\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u306f\u5f53\u7136\u3067\u3059\u3002\u307e\u305f\u7bc4\u56f2\u304c\u9006\u306b\u306a\u308b\u5834\u5408\u3001\u30de\u30a4\u30ca\u30b9\u3092\u52a0\u3048\u307e\u3057\u3087\u3046\u3002\u7a4d\u5206\u5f8c\u306e\u5f15\u304d\u7b97\u306e\u9806\u756a\u304c\u9006\u306b\u306a\u308b\u305f\u3081\u3001\u7b49\u53f7\u3067\u3064\u306a\u3050\u305f\u3081\u306b\u306f\u30de\u30a4\u30ca\u30b9\u3092\u52a0\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{a}^{b} f(x) dx=-\\displaystyle \\int_{b}^{a} f(x) dx\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u304c\u7a4d\u5206\u3067\u3042\u308b\u305f\u3081\u3001\u9014\u4e2d\u3067\u7bc4\u56f2\u3092\u533a\u5207\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u533a\u5207\u3063\u305f\u5834\u6240\u3092\u7528\u3044\u3066\u8db3\u3057\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{a}^{b} f(x) dx\\)\\(=\\displaystyle \\int_{a}^{c} f(x) dx\\)\\(+\\displaystyle \\int_{c}^{b} f(x) dx\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/jd16.jpg\" alt=\"\" width=\"463\" height=\"293\" class=\"aligncenter size-full wp-image-11651\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u306e\u7b54\u3048\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{1}^{2} \\left(x^3+\\displaystyle\\frac{1}{\\sqrt{x}}\\right) dx\\)<\/li>\n<\/ul>\n<p>\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle \\int_{1}^{2} \\left(x^3+\\displaystyle\\frac{1}{\\sqrt{x}}\\right) dx\\)<\/p>\n<p>\\(=\\displaystyle \\int_{1}^{2} x^3 dx\\)\\(+\\displaystyle \\int_{1}^{2} x^{-\\frac{1}{2}} dx\\)<\/p>\n<p>\\(=\\left[\\displaystyle\\frac{1}{3+1}x^{3+1}\\right]_1^2\\)\\(+\\left[\\displaystyle\\frac{1}{-\\displaystyle\\frac{1}{2}+1}x^{-\\frac{1}{2}+1}\\right]_1^2\\)<\/p>\n<p>\\(=\\left[\\displaystyle\\frac{1}{4}x^{4}\\right]_1^2\\)\\(+\\left[2x^{\\frac{1}{2}}\\right]_1^2\\)<\/p>\n<p>\\(=\\left[\\displaystyle\\frac{1}{4}x^{4}\\right]_1^2\\)\\(+[2\\sqrt{x}]_1^2\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{4}(2^4-1^4)+2(\\sqrt{2}-1)\\)<\/p>\n<p>\\(=\\displaystyle\\frac{7}{4}+2\\sqrt{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u5b9a\u7a4d\u5206\u3067\u8868\u3055\u308c\u305f\u95a2\u6570\u306e\u8a08\u7b97<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5b9a\u7a4d\u5206\u3067\u8868\u3055\u308c\u305f\u95a2\u6570\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u95a2\u6570\u306e\u4e2d\u306b\u7a4d\u5206\u3092\u542b\u3080\u5f0f\u306e\u8a08\u7b97\u3092\u884c\u3044\u307e\u3059\u3002\u5b9f\u969b\u306b\u4f8b\u984c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u6b21\u306e\u5f0f\u3092\u6e80\u305f\u3059\\(f(x)\\)\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(f(x)=x^2+2\\displaystyle \\int_{0}^{1} f(x) dx\\)<\/li>\n<\/ul>\n<p>\u7a4d\u5206\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u306b\u3057\u3066\u3082\u3001\\(f(x)\\)\u306f\u3053\u308c\u304b\u3089\u6c42\u3081\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u5f0f\u3067\u3042\u308b\u305f\u3081\u3001\u7a4d\u5206\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\\(\\displaystyle \\int_{0}^{1} f(x) dx\\)\u306b\u7740\u76ee\u3057\u307e\u3057\u3087\u3046\u3002\\(\\displaystyle \\int_{0}^{1} f(x) dx\\)\u306f\u7279\u5b9a\u306e\u7bc4\u56f2\u306e\u9762\u7a4d\u3092\u793a\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001<span style=\"color: #ff0000;\">\\(\\displaystyle \\int_{0}^{1} f(x) dx\\)\u306f\u5b9a\u6570\u3067\u3059\u3002<\/span><\/p>\n<p>\\(\\displaystyle \\int_{0}^{1} f(x) dx\\)\u306f\u660e\u78ba\u306a\u5024\u3067\u3042\u308b\u305f\u3081\u3001\\(\\displaystyle \\int_{0}^{1} f(x) dx=a\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f(x)=x^2+2a\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u5f0f\u306f\u4e8c\u6b21\u95a2\u6570\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u307e\u305f\\(f(x)=x^2+2a\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(\\displaystyle \\int_{0}^{1} f(x) dx=a\\)\u306b\u4ee3\u5165\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\int_{0}^{1} f(x) dx=a\\)<\/p>\n<p>\\(\\displaystyle \\int_{0}^{1} (x^2+2a) dx=a\\)<\/p>\n<p>\\(\\left[\\displaystyle\\frac{1}{3}x^3+2ax\\right]_0^1=a\\)<\/p>\n<p>\\(\\left(\\displaystyle\\frac{1}{3}+2a\\right)-0=a\\)<\/p>\n<p>\\(a=-\\displaystyle\\frac{1}{3}\\)<\/p>\n<p>\\(a=-\\displaystyle\\frac{1}{3}\\)\u3068\u308f\u304b\u3063\u305f\u305f\u3081\u3001\\(f(x)=x^2-\\displaystyle\\frac{2}{3}\\)\u3068\u8a08\u7b97\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u7bc4\u56f2\u306b\u5909\u6570\u3092\u542b\u3080\u7a4d\u5206\u3068\u95a2\u6570\uff1a\u5fae\u5206\u306e\u5229\u7528<\/h3>\n<p>\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3067\u306f\u3001\u5b9a\u7a4d\u5206\u3068\u5fae\u5206\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3057\u305f\u554f\u984c\u3082\u3072\u3093\u3071\u3093\u306b\u51fa\u984c\u3055\u308c\u307e\u3059\u3002\u5b9a\u7a4d\u5206\u306e\u7bc4\u56f2\u306b\u5909\u6570\u3092\u542b\u3080\u5834\u5408\u3001\u5fae\u5206\u3059\u308b\u3053\u3068\u3067\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u524d\u8ff0\u306e\u901a\u308a\u3001\u5fae\u5206\u3068\u7a4d\u5206\u306f\u89aa\u305b\u304d\u95a2\u4fc2\u306b\u3042\u308a\u307e\u3059\u3002\u7a4d\u5206\u3057\u305f\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u3068\u3001\u95a2\u6570\u306f\u5143\u306b\u623b\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u300c\u5b9a\u7a4d\u5206\u3092\u5fae\u5206\u3059\u308b\u5834\u5408\u300d\u306f\u3069\u3046\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u306e\u554f\u984c\u3067\u78ba\u8a8d\u3057\u305f\u901a\u308a\u3001\u5b9a\u7a4d\u5206\u306f\u5b9a\u6570\u3067\u3059\u3002<span style=\"color: #0000ff;\">\u5b9a\u6570\u3092\u5fae\u5206\u3059\u308b\u30680\u306b\u306a\u308a\u307e\u3059\u3002<\/span>\u4f8b\u3068\u3057\u3066\u3001\\(\\displaystyle \\int_{1}^{0} (2x+1) dx\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\int_{1}^{0} (2x+1) dx\\)<\/p>\n<p>\\(=\\left[x^2+x\\right]_0^1\\)<\/p>\n<p>\\(=(1+1)-0\\)<\/p>\n<p>\\(=2\\)<\/p>\n<p>2\u306b\u5bfe\u3057\u3066\\(x\\)\u3067\u5fae\u5206\u3059\u308b\u30680\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\\(\\displaystyle \\int_{1}^{x} (2t+1) dt\\)\u3092\u5fae\u5206\u3059\u308b\u5834\u5408\u306f\u3069\u3046\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u3068\u306f\u7570\u306a\u308a\u3001\u5b9a\u7a4d\u5206\u306e\u7bc4\u56f2\u306b\u5909\u6570\\(x\\)\u3092\u542b\u307f\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5fae\u5206\u3092\u3059\u308b\u3053\u3068\u3067\\(2x+1\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u5b9f\u969b\u306b\u8a08\u7b97\u3092\u3057\u3066\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\int_{1}^{x} (2t+1) dt\\)<\/p>\n<p>\\(=\\left[t^2+t\\right]_0^x\\)<\/p>\n<p>\\(=(x^2+x)-0\\)<\/p>\n<p>\\(=x^2+x\\)<\/p>\n<p>\\(x^2+x\\)\u3092\u5fae\u5206\u3059\u308b\u3068\\(2x+1\\)\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001<span style=\"color: #0000ff;\">\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u3067\u7bc4\u56f2\u306b\u5909\u6570\u3092\u542b\u3080\u5834\u5408\u3001\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7a4d\u5206\u8a18\u53f7\u3092\u53d6\u308a\u53bb\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/span>\u305d\u306e\u305f\u3081\\(\\displaystyle \\int_{a}^{x} f(t) dt\\)\u3084\\(\\displaystyle \\int_{x}^{a} f(t) dt\\)\u306e\u3088\u3046\u306b\u3001\u7bc4\u56f2\u306b\u5909\u6570\\(x\\)\u3092\u542b\u3080\u5834\u5408\u306f\u5fae\u5206\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u95a2\u6570\\(f(x)\\)\u3068\u5b9a\u6570\\(a\\)\u306e\u5024\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{x}^{a} f(t) dt=-x^2+x+2\\)<\/li>\n<\/ul>\n<p>\u4e21\u8fba\u3092\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7a4d\u5206\u8a18\u53f7\u3092\u6d88\u53bb\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u5148\u307b\u3069\u306e\u8aac\u660e\u3068\u306f\u7570\u306a\u308a\u3001\u7bc4\u56f2\u306f\u5909\u6570\\(x\\)\u304b\u3089\u5b9a\u6570\\(a\\)\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u8a08\u7b97\u3059\u308b\u7bc4\u56f2\u3092\u5b9a\u6570\\(a\\)\u304b\u3089\u5909\u6570\\(x\\)\u306b\u5909\u3048\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\u5148\u307b\u3069\u306e\u5f0f\u3092\u4ee5\u4e0b\u306e\u5f0f\u3078\u5909\u5f62\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{a}^{x} f(t) dt=x^2-x-2\\)<\/li>\n<\/ul>\n<p>\u6b21\u306b\u3001\u4e21\u8fba\u3092\u5fae\u5206\u3057\u307e\u3057\u3087\u3046\u3002\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u306e\u3067\u3042\u308c\u3070\u3001\u4e21\u8fba\u3092\u5fae\u5206\u3057\u305f\u5f8c\u3067\u3042\u3063\u3066\u3082\u5f0f\u304c\u540c\u3058\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u5fae\u5206\u3059\u308b\u3068\u3001\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f(x)=2x-1\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u95a2\u6570\\(f(x)=2x-1\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u6b21\u306b\u3001\u5b9a\u6570\\(a\\)\u306e\u5024\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\u3067\u8aac\u660e\u3057\u305f\u901a\u308a\u3001\u7bc4\u56f2\u304c0\u306e\u5834\u5408\u306f\u7b54\u3048\uff08\u9762\u7a4d\uff09\u304c\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\\(x=a\\)\u306e\u5834\u5408\u3001\u7b54\u3048\u306f\u30bc\u30ed\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\int_{a}^{a} f(t) dt=a^2-a-2\\)\\(=0\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a^2-a-2=0\\)<\/p>\n<p>\\((a+1)(a-2)=0\\)<\/p>\n<p>\\(a=-1,2\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5b9a\u6570\\(a\\)\u306e\u5024\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u5fae\u5206\u3068\u7a4d\u5206\u306e\u95a2\u4fc2\u306b\u52a0\u3048\u3066\u3001\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7a4d\u5206\u306e\u516c\u5f0f\u3092\u899a\u3048\u3001\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u3059\u308b<\/h2>\n<p>\u5fae\u5206\u306e\u9006\u304c\u7a4d\u5206\u3067\u3059\u3002\u305f\u3060\u5fae\u5206\u306e\u516c\u5f0f\u306f\u899a\u3048\u3084\u3059\u3044\u3082\u306e\u306e\u3001\u7a4d\u5206\u306e\u516c\u5f0f\u306f\u5c11\u3057\u8907\u96d1\u3067\u3059\u3002\u305d\u3053\u3067\u516c\u5f0f\u3092\u899a\u3048\u3001\u7a4d\u5206\u306b\u6163\u308c\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u95a2\u6570\u3092\u7a4d\u5206\u3059\u308b\u3068\u304d\u3001\u4e0d\u5b9a\u7a4d\u5206\u3092\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3067\u5f97\u305f\u3044\u9762\u7a4d\u306e\u7bc4\u56f2\u304c\u6c7a\u307e\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u5b9a\u7a4d\u5206\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u307e\u305f\u3001\u5fdc\u7528\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5b9a\u7a4d\u5206\u3092\u3059\u308b\u5834\u5408\u3001\u5f97\u3089\u308c\u308b\u7b54\u3048\u306f\u5b9a\u6570\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5b9a\u7a4d\u5206\u306b\u3088\u3063\u3066\u8868\u3055\u308c\u305f\u95a2\u6570\u306e\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u4e00\u65b9\u3067\u306e\u7bc4\u56f2\u306b\u5909\u6570\u3092\u542b\u3080\u5834\u5408\u3001\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u95a2\u6570\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u6570\u5b66\u3067\u91cd\u8981\u306a\u5185\u5bb9\u304c\u7a4d\u5206\u3067\u3059\u3002\u5fae\u5206\u3092\u5b66\u3079\u3070\u3001\u7a4d\u5206\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u4e0d\u5b9a\u7a4d\u5206\u3068\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\u3092\u899a\u3048\u3001\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5fae\u5206\u306e\u53cd\u5bfe\u304c\u7a4d\u5206\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u7a4d\u5206\u3092\u5b66\u3076\u3068\u304d\u3001\u4e8b\u524d\u306b\u5fae\u5206\u3092\u7406\u89e3\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u5fae\u5206\u306e\u53cd\u5bfe\u3092\u516c\u5f0f\u3068\u3057\u3066\u899a\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7a4d\u5206\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002 \u306a\u304a\u3001\u7279\u5b9a\u306e\u7bc4\u56f2\u3092\u6307\u5b9a\u305b\u305a\u306b\u7a4d\u5206\u3092\u3059\u308b\u5834\u5408\u3001\u4e0d\u5b9a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11583,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-11552","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\/11552","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=11552"}],"version-history":[{"count":15,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11552\/revisions"}],"predecessor-version":[{"id":11676,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11552\/revisions\/11676"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/11583"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=11552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=11552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=11552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}