{"id":5316,"date":"2025-01-08T19:58:21","date_gmt":"2025-01-08T10:58:21","guid":{"rendered":"https:\/\/torisetudy.com\/?p=5316"},"modified":"2026-03-09T17:49:13","modified_gmt":"2026-03-09T08:49:13","slug":"%e7%a9%8d%e5%88%86%e6%b3%95","status":"publish","type":"post","link":"https:\/\/torisetudy.com\/?p=5316","title":{"rendered":"\u7a4d\u5206\u6cd5"},"content":{"rendered":"\n<div id=\"toc_container\" class=\"no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u4e0d\u5b9a\u7a4d\u5206<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u5b9a\u7a4d\u5206<\/a><\/li><\/ul><\/div>\n<h2 class=\"wp-block-heading\"><span id=\"i\">\u4e0d\u5b9a\u7a4d\u5206<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u539f\u59cb\u95a2\u6570\u3068\u7a4d\u5206\u5b9a\u6570<\/h3>\n\n\n\n<p>\u95a2\u6570 $f(x)$ \u306b\u5bfe\u3057\u3066\uff0c\u5fae\u5206\u3059\u308b\u3068 $f(x)$ \u306b\u306a\u308b\u95a2\u6570\u3092 $F(x)$ \u3068\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\uff0c\u95a2\u6570 $F(x)$ \u306f\uff0c$F\\mskip 1mu\\prime (x)=f(x)$ \u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u3053\u306e\u95a2\u6570 $F(x)$ \u3092\uff0c$f(x)$ \u306e<span class=\"st-mymarker-s\">\u539f\u59cb\u95a2\u6570<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>$f(x)=3x^2$ \u3068\u3059\u308b\u3068\u304d\uff0c$f(x)$ \u306e\u539f\u59cb\u95a2\u6570 $F(x)$ \u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u5fae\u5206\u3057\u3066 $3x^2$ \u3068\u306a\u308b\u95a2\u6570\u306f\uff0c\u5b9f\u306f\u305f\u304f\u3055\u3093\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$(x^3)\\mskip 1mu\\prime =3x^2,\\ (x^3+5)\\mskip 1mu\\prime =3x^2,\\ (x^3-10)\\mskip 1mu\\prime =3x^2$$\u3068\u306a\u308b\u3053\u3068\u304b\u3089\uff0c$x^3$\uff0c$x^3+5$\uff0c$x^3-10$ \u306a\u3069\u306f\u3059\u3079\u3066 $F(x)$ \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3089\u306f\uff0c\u5b9a\u6570$C$ \u3092\u7528\u3044\u308b\u3053\u3068\u3067\uff0c$F(x)=x^3+C$ \u3068\u304b\u3051\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u5b9a\u6570 $C$ \u306f\u5fae\u5206\u3057\u305f\u969b\u306b $0$ \u306b\u306a\u308a\u307e\u3059\u306e\u3067\uff0c${F(x)+C}&#8217;=F\\mskip 1mu\\prime (x)=f(x)$ \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u5b9a\u6570 $C$ \u306e\u3053\u3068\u3092<span class=\"st-mymarker-s\">\u7a4d\u5206\u5b9a\u6570<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u4ee5\u4e0a\u3092\u307e\u3068\u3081\u308b\u3068\uff0c<\/p>\n\n\n\n<p>$$\\int f(x)\\dx=F(x)+C\\quad \\stext{\uff08$C$ \u306f\u7a4d\u5206\u5b9a\u6570\uff09}$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\uff0c\u4e0d\u5b9a\u7a4d\u5206\u3092\u6c42\u3081\u308b\u3053\u3068\u3092<span class=\"st-mymarker-s\">\u7a4d\u5206\u3059\u308b<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u516c\u5f0f\u3068\u6027\u8cea<\/h3>\n\n\n\n<p>\u95a2\u6570\u3092\u7a4d\u5206\u3059\u308b\u306b\u306f\uff0c\u5fae\u5206\u6cd5\u306e\u9006\u8a08\u7b97\u3092\u3059\u308c\u3070\u3088\u3044\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u30dd\u30a4\u30f3\u30c8<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">\u81ea\u7136\u6570 $n$ \u306b\u3064\u3044\u3066\uff0c $x^n$ \u306f\u6b21\u306e\u901a\u308a\u306b\u7a4d\u5206\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\int x^n\\dx=\\bun{1}{n+1}x^{n+1}+C\\ \\stext{\uff08$n$ \u306f $0$ \u307e\u305f\u306f\u6b63\u306e\u6574\u6570\uff09}$$<\/p>\n<\/div><\/div>\n\n\n\n<p>\u4e0d\u5b9a\u7a4d\u5206\u306f\uff0c\u5fae\u5206\u6cd5\u306e\u9006\u8a08\u7b97\u3067\u3059\u304b\u3089\uff0c\u4ee5\u4e0b\u306e\u6027\u8cea\u3082\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u4e0d\u5b9a\u7a4d\u5206\u306e\u6027\u8cea<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$k,\\,l$ \u3092\u5b9a\u6570\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\begin{aligned}&amp;\\stext{\u2460}\\ \\int kf(x)\\dx=k\\int f(x)\\dx\\\\&amp;\\stext{\u2461}\\int {f(x)+g(x)}\\dx=\\int f(x)\\dx+\\int g(x)\\dx\\end{aligned}$$<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">\u2460\uff0c\u2461 \u3088\u308a\uff0c<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\stext{\u2462}\\int {kf(x)+lg(x)}\\dx=k\\int f(x)\\dx+l\\int g(x)\\dx$$<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span id=\"i-2\">\u5b9a\u7a4d\u5206<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97<\/h3>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon1 clearfix\"><div class=\"st-kaiwa-face\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name\">\u7fbd\u767d<\/div><\/div><div class=\"st-kaiwa-area\"><div class=\"st-kaiwa-hukidashi\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>\u3053\u3053\u304b\u3089\u306f\uff0c\u53b3\u5bc6\u306a\u8a3c\u660e\u3092\u7701\u7565\u3057\u3066\u300c\u5b9a\u7a4d\u5206\u300d\u3068\u3044\u3046\u6982\u5ff5\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div><\/div><\/div><\/div>\n\n\n\n<p>$f(x)$ \u306e\u4e0d\u5b9a\u7a4d\u5206\u3092 $F(x)$ \u3068\u3057\uff0c$F(b)-F(a)$ \u3092 $\\Bigl[F(x)\\Bigr]_a^b$ \u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\uff0c<\/p>\n\n\n\n<p>$$\\int_a^b f(x)\\dx=\\Bigl[F(x)\\Bigr]_a^b=F(b)-F(a)$$\u3068\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u3053\u308c\u3092\uff0c$f(x)$ \u306e $a$ \u304b\u3089 $b$ \u307e\u3067\u306e<span class=\"st-mymarker-s\">\u5b9a\u7a4d\u5206<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u305f\u3068\u3048\u3070\uff0c<\/p>\n\n\n\n<p>$$\\begin{aligned}\\int_1^3(3x^2-2x)\\dx&amp;=\\Bigl[x^3-x^2\\Bigr]_1^3\\\\&amp;=(3^3-3^2)-(1^3-1^2)\\\\&amp;=18\\end{aligned}$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305f\uff0c$\\displaystyle\\int_a^bf(x)\\dx$ \u306b\u304a\u3044\u3066\uff0c$a$ \u3092\u5b9a\u7a4d\u5206\u306e<span class=\"st-mymarker-s\">\u4e0b\u7aef<\/span>\uff0c$b$ \u3092<span class=\"st-mymarker-s\">\u4e0a\u7aef<\/span>\u3068\u3044\u3044\u307e\u3059\u3002\u3053\u306e\u5b9a\u7a4d\u5206\u3092\u6c42\u3081\u308b\u3053\u3068\u3092\uff0c<span class=\"st-mymarker-s-b\">$f(x)$ \u3092 $a$ \u304b\u3089 $b$ \u307e\u3067\u7a4d\u5206\u3059\u308b<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9a\u7a4d\u5206\u306e\u6027\u8cea<\/h3>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon1 clearfix\"><div class=\"st-kaiwa-face\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name\">\u7fbd\u767d<\/div><\/div><div class=\"st-kaiwa-area\"><div class=\"st-kaiwa-hukidashi\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>\u3053\u306e\u8a08\u7b97\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u304b\u306f\u3055\u3066\u304a\u304d\uff0c\u5b9a\u7a4d\u5206\u306e\u6027\u8cea\u3092\u62bc\u3055\u3048\uff0c\u8a08\u7b97\u306e\u7df4\u7fd2\u3092\u3057\u3066\u3044\u304f\u3053\u3068\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<\/div><\/div><\/div><\/div>\n\n\n\n<p>\u5b9a\u7a4d\u5206\u306e\u8a08\u7b97\u306b\u304a\u3044\u3066\u3082\uff0c\u4e0d\u5b9a\u7a4d\u5206\u3068\u540c\u69d8\u306b\u4ee5\u4e0b\u306e\u6027\u8cea\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u5b9a\u7a4d\u5206\u306e\u6027\u8cea \u305d\u306e1<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$k,\\,l$ \u3092\u5b9a\u6570\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\begin{aligned}&amp;\\stext{\u2460}\\ \\int_a^b kf(x)\\dx=k\\int_a^b f(x)\\dx\\\\&amp;\\stext{\u2461}\\ \\int_a^b {f(x)+g(x)}\\dx=\\int_a^b f(x)\\dx+\\int_a^b g(x)\\dx\\end{aligned}$$<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">\u2460\uff0c\u2461 \u3088\u308a\uff0c<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\stext{\u2462}\\ \\int_a^b {kf(x)+lg(x)}\\dx=k\\int_a^b f(x)\\dx+l\\int_a^b g(x)\\dx$$<\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u6b211 \u4e0d\u5b9a\u7a4d\u52062 \u5b9a\u7a4d\u5206 \u4e0d\u5b9a\u7a4d\u5206 \u539f\u59cb\u95a2\u6570\u3068\u7a4d\u5206\u5b9a\u6570 \u95a2\u6570 $f(x)$ \u306b\u5bfe\u3057\u3066\uff0c\u5fae\u5206\u3059\u308b\u3068 $f(x)$ \u306b\u306a\u308b\u95a2\u6570\u3092 $F(x)$ \u3068\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\uff0c\u95a2\u6570 $F(x)$ \u306f\uff0c$F\\mski &#8230; <\/p>\n","protected":false},"author":1,"featured_media":5333,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[37,32],"tags":[],"class_list":["post-5316","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-calculus","category-32"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5316"}],"collection":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5316"}],"version-history":[{"count":14,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5316\/revisions"}],"predecessor-version":[{"id":5499,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5316\/revisions\/5499"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/media\/5333"}],"wp:attachment":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5316"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5316"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}