{"id":4234,"date":"2013-12-11T06:00:09","date_gmt":"2013-12-10T21:00:09","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4234"},"modified":"2014-09-10T16:52:06","modified_gmt":"2014-09-10T07:52:06","slug":"post-4234","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4234","title":{"rendered":"\u7a4d\u5206"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><h3>\u7a4d\u5206<\/h3>\n<p>\u3000\u3042\u308b\u95a2\u6570\u306b\u3064\u3044\u3066 dy\/dx = f(x) \u3067\u3042\u308b\u6642\uff0cy \u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cint+f%28x%29dx&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\int f(x)dx' title='\\displaystyle \\int f(x)dx' class='latex' \/><\/p>\n<p>\u3000<img src='https:\/\/s0.wp.com\/latex.php?latex=f%28x%29+%3D+%5Cfrac%7Bd%7D%7Bdx%7DF%28x%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='f(x) = \\frac{d}{dx}F(x)' title='f(x) = \\frac{d}{dx}F(x)' class='latex' \/> \u306e\u6642\uff0c\u7a4d\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cint_a%5Eb+f%28x%29dx+%3D+F%28b%29+-+F%28a%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\int_a^b f(x)dx = F(b) - F(a)' title='\\displaystyle \\int_a^b f(x)dx = F(b) - F(a)' class='latex' \/><\/p>\n<h3>\u7a4d\u5206\u516c\u5f0f<\/h3>\n<p>\u3000\u95a2\u6570 u, v \u304a\u3088\u3073\u5b9a\u6570 a, b, c, p \u306b\u3064\u3044\u3066\u4e0b\u8a18\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle++++%5Cint+%28u+%5Cpm+v%29dx+%3D+%5Cint+u+dx+%5Cpm+%5Cint+v+dx%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+cu+dx+%3D+c%5Cint+u+dx+%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+u%5Cleft%28%5Cfrac%7Bdv%7D%7Bdx%7D%5Cright%29+%3D+uv+-+%5Cint+v+%5Cleft%28%5Cfrac%7Bdu%7D%7Bdx%7D%5Cright%29dx+%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+u+dv+%3D+uv+-+%5Cint+v+du+%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+F%28u%28x%29%29dx+%3D+%5Cint+F%28w%29%5Cfrac%7Bdw%7D%7Bdw%2Fdx%7D%2C%5C+w+%3D+u%28x%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle    \\int (u \\pm v)dx = \\int u dx \\pm \\int v dx\\\\\\vspace{0.2 in}   \\int cu dx = c\\int u dx \\\\\\vspace{0.2 in}   \\int u\\left(\\frac{dv}{dx}\\right) = uv - \\int v \\left(\\frac{du}{dx}\\right)dx \\\\\\vspace{0.2 in}   \\int u dv = uv - \\int v du \\\\\\vspace{0.2 in}   \\int F(u(x))dx = \\int F(w)\\frac{dw}{dw\/dx},\\ w = u(x)' title='\\displaystyle    \\int (u \\pm v)dx = \\int u dx \\pm \\int v dx\\\\\\vspace{0.2 in}   \\int cu dx = c\\int u dx \\\\\\vspace{0.2 in}   \\int u\\left(\\frac{dv}{dx}\\right) = uv - \\int v \\left(\\frac{du}{dx}\\right)dx \\\\\\vspace{0.2 in}   \\int u dv = uv - \\int v du \\\\\\vspace{0.2 in}   \\int F(u(x))dx = \\int F(w)\\frac{dw}{dw\/dx},\\ w = u(x)' class='latex' \/>\n<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle++++%5Cint+u%5Ep+du+%3D+%5Cfrac%7Bu%5E%7Bp%2B1%7D%7D%7Bp%2B1%7D%2C%5C+p+%5Cneq+-1%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+u%5E%7B-1%7Ddu+%3D+%5Cint+%5Cfrac%7Bdu%7D%7Bu%7D+%3D+%5Cln+u%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+a%5Eu+du+%3D+%5Cfrac%7Ba%5Eu%7D%7B%5Cln+a%7D%2C%5C+a+%5Cneq+0%2C%5C+1%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+e%5Eu+du+%3D+e%5Eu&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle    \\int u^p du = \\frac{u^{p+1}}{p+1},\\ p \\neq -1\\\\\\vspace{0.2 in}   \\int u^{-1}du = \\int \\frac{du}{u} = \\ln u\\\\\\vspace{0.2 in}   \\int a^u du = \\frac{a^u}{\\ln a},\\ a \\neq 0,\\ 1\\\\\\vspace{0.2 in}   \\int e^u du = e^u' title='\\displaystyle    \\int u^p du = \\frac{u^{p+1}}{p+1},\\ p \\neq -1\\\\\\vspace{0.2 in}   \\int u^{-1}du = \\int \\frac{du}{u} = \\ln u\\\\\\vspace{0.2 in}   \\int a^u du = \\frac{a^u}{\\ln a},\\ a \\neq 0,\\ 1\\\\\\vspace{0.2 in}   \\int e^u du = e^u' class='latex' \/>\n<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle++++%5Cint+%5Csin+u%5C+du+%3D+-%5Ccos%7Bu%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+%5Ccos+u%5C+du+%3D+%5Csin%7Bu%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+%5Ctan+u%5C+du+%3D+-%5Cln+%5Ccos%7Bu%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+e%5E%7Bau%7D%5Csin%7Bbu%7D%5C+du+%3D+%5Cfrac%7Be%5E%7Bau%7D%28a%5C+%5Csin%7Bbu%7D-+b%5C+%5Ccos%7Bbu%7D%29%7D%7Ba%5E2+%2B+b%5E2%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+e%5E%7Bau%7D%5Ccos%7Bbu%7D%5C+du+%3D+%5Cfrac%7Be%5E%7Bau%7D%28a%5C+%5Ccos%7Bbu%7D%2B+b%5C+%5Csin%7Bbu%7D%29%7D%7Ba%5E2+%2B+b%5E2%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+%5Cfrac%7Bdu%7D%7B%5Csqrt%7Ba%5E2+-+u%5E2%7D%7D+%3D+%5Csin%5E%7B-1%7D%5Cfrac%7Bu%7D%7Ba%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+%5Cfrac%7Bdu%7D%7Bu%5E2+%2B+a%5E2%7D+%3D+%5Cfrac%7B1%7D%7Ba%7D%5Ctan%5E%7B-1%7D%5Cfrac%7Bu%7D%7Ba%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+%5Cfrac%7Bdu%7D%7B%5Csqrt%7Bu%5E2+-+a%5E2%7D%7D+%3D+%5Cln%28u+%2B+%5Csqrt%7Bu%5E2+-+a%5E2%7D%29%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cint+%5Cfrac%7Bdu%7D%7B%5Csqrt%7Bu%5E2+%2B+a%5E2%7D%7D+%3D+%5Cln%28u+%2B+%5Csqrt%7Bu%5E2+%2B+a%5E2%7D%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle    \\int \\sin u\\ du = -\\cos{u}\\\\\\vspace{0.2 in}   \\int \\cos u\\ du = \\sin{u}\\\\\\vspace{0.2 in}   \\int \\tan u\\ du = -\\ln \\cos{u}\\\\\\vspace{0.2 in}   \\int e^{au}\\sin{bu}\\ du = \\frac{e^{au}(a\\ \\sin{bu}- b\\ \\cos{bu})}{a^2 + b^2}\\\\\\vspace{0.2 in}   \\int e^{au}\\cos{bu}\\ du = \\frac{e^{au}(a\\ \\cos{bu}+ b\\ \\sin{bu})}{a^2 + b^2}\\\\\\vspace{0.2 in}   \\int \\frac{du}{\\sqrt{a^2 - u^2}} = \\sin^{-1}\\frac{u}{a}\\\\\\vspace{0.2 in}   \\int \\frac{du}{u^2 + a^2} = \\frac{1}{a}\\tan^{-1}\\frac{u}{a}\\\\\\vspace{0.2 in}   \\int \\frac{du}{\\sqrt{u^2 - a^2}} = \\ln(u + \\sqrt{u^2 - a^2})\\\\\\vspace{0.2 in}   \\int \\frac{du}{\\sqrt{u^2 + a^2}} = \\ln(u + \\sqrt{u^2 + a^2})' title='\\displaystyle    \\int \\sin u\\ du = -\\cos{u}\\\\\\vspace{0.2 in}   \\int \\cos u\\ du = \\sin{u}\\\\\\vspace{0.2 in}   \\int \\tan u\\ du = -\\ln \\cos{u}\\\\\\vspace{0.2 in}   \\int e^{au}\\sin{bu}\\ du = \\frac{e^{au}(a\\ \\sin{bu}- b\\ \\cos{bu})}{a^2 + b^2}\\\\\\vspace{0.2 in}   \\int e^{au}\\cos{bu}\\ du = \\frac{e^{au}(a\\ \\cos{bu}+ b\\ \\sin{bu})}{a^2 + b^2}\\\\\\vspace{0.2 in}   \\int \\frac{du}{\\sqrt{a^2 - u^2}} = \\sin^{-1}\\frac{u}{a}\\\\\\vspace{0.2 in}   \\int \\frac{du}{u^2 + a^2} = \\frac{1}{a}\\tan^{-1}\\frac{u}{a}\\\\\\vspace{0.2 in}   \\int \\frac{du}{\\sqrt{u^2 - a^2}} = \\ln(u + \\sqrt{u^2 - a^2})\\\\\\vspace{0.2 in}   \\int \\frac{du}{\\sqrt{u^2 + a^2}} = \\ln(u + \\sqrt{u^2 + a^2})' class='latex' \/><\/p>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0071635408\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u7a4d\u5206 \u3000\u3042\u308b\u95a2\u6570\u306b\u3064\u3044\u3066 dy\/dx = f(x) \u3067\u3042\u308b\u6642\uff0cy \u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3055\u308c\u307e\u3059\uff0e \u3000 \u306e\u6642\uff0c\u7a4d\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e \u7a4d\u5206\u516c\u5f0f \u3000\u95a2\u6570 u, v \u304a\u3088\u3073\u5b9a\u6570 a, b, c, p \u306b\u3064\u3044\u3066\u4e0b\u8a18\u304c\u6210\u308a\u7acb &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4234\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u7a4d\u5206&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4234","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4234","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4234"}],"version-history":[{"count":23,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4234\/revisions"}],"predecessor-version":[{"id":6811,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4234\/revisions\/6811"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}