{"id":101,"date":"2008-01-06T14:10:02","date_gmt":"2008-01-06T05:10:02","guid":{"rendered":"http:\/\/njet.oops.jp\/wordpress\/2008\/01\/06\/%e6%a5%95%e5%86%86%e9%96%a2%e6%95%b0%e3%81%ae%e8%a9%b12\/"},"modified":"2008-01-06T14:10:02","modified_gmt":"2008-01-06T05:10:02","slug":"%e6%a5%95%e5%86%86%e9%96%a2%e6%95%b0%e3%81%ae%e8%a9%b12","status":"publish","type":"post","link":"https:\/\/njet.oops.jp\/wordpress\/2008\/01\/06\/%e6%a5%95%e5%86%86%e9%96%a2%e6%95%b0%e3%81%ae%e8%a9%b12\/","title":{"rendered":"\u6955\u5186\u95a2\u6570\u306e\u8a71(2)"},"content":{"rendered":"


\n\u30ec\u30e0\u30cb\u30b9\u30b1\u30fc\u30c8\u306e\u7a4d\u5206 $\\int \\frac{dx}{\\sqrt{1-x^4}}$ \u306e\u3088\u3046\u306b\uff0c3\u6b21\u5f0f\uff0c4\u6b21\u5f0f\u306e\u5e73\u65b9\u6839\u3092\u542b\u3080\u7a4d\u5206\u306f\uff0c
\n\u7dcf\u79f0\u3057\u3066\u6955\u5186\u7a4d\u5206\u3068\u547c\u3070\u308c\u308b\u3002
\n\u6955\u5186\u306e\u5f27\u9577\u304c\u3053\u306e\u30bf\u30a4\u30d7\u306e\u7a4d\u5206\u306b\u306a\u308b\u3053\u3068\u304c\u540d\u524d\u306e\u7531\u6765\u3067\u3042\u308b\u304c\uff0c\u305d\u308c\u4ee5\u5916\u306b\u6955\u5186\u3068\u306e\u95a2\u4fc2\u306f\u7279\u306b\u306a\u3044\u3002
\n\u6955\u5186\u306b\u7279\u6709\u306e\u7a4d\u5206\u3068\u3044\u3046\u308f\u3051\u3067\u3082\u306a\u3044\u304b\u3089\uff0c\u5b9f\u306f\u3042\u307e\u308a\u826f\u304f\u306a\u3044\u540d\u79f0\u3068\u3082\u8a00\u3048\u308b\u3002
\n\u305d\u308c\u306f\u3068\u3082\u304b\u304f\uff0c\u3053\u306e\u6955\u5186\u7a4d\u5206\uff0c\u826f\u304f\u77e5\u3089\u308c\u305f\u521d\u7b49\u95a2\u6570(\u6709\u7406\u95a2\u6570\uff0c\u4e09\u89d2\u95a2\u6570\uff0c\u6307\u6570\u95a2\u6570\uff0c\u5bfe\u6570\u95a2\u6570\uff0c\u306a\u3069\u306a\u3069)\u3067\u306f\u8868\u305b\u306a\u3044\u3002
\n\u3053\u308c\u306b\u5bfe\u3057\u3066\uff0c2\u6b21\u5f0f\u306e\u5e73\u65b9\u6839\u3092\u542b\u3080\u7a4d\u5206\u306f\u521d\u7b49\u95a2\u6570\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u4f8b\u3048\u3070\uff0c
\n\\[ \\int_{0}^{x} \\frac{dx}{\\sqrt{x^2+1}}=\\log(x+\\sqrt{x^2+1}), \\qquad
\n \\int_{0}^{x} \\frac{dx}{\\sqrt{1-x^2}}=\\arcsin x \\]
\n\u3067\u3042\u308b\u3002
\n2\u756a\u76ee\u306e\u7a4d\u5206\u306f\u30ec\u30e0\u30cb\u30b9\u30b1\u30fc\u30c8\u306e\u7a4d\u5206\u3068\u5f62\u304c\u4f3c\u3066\u3044\u308b\u304c\uff0c\u3053\u308c\u304c\u4e00\u3064\u306e\u30dd\u30a4\u30f3\u30c8\u3068\u306a\u308b\u3002<\/p>\n

\u3055\u3066\uff0c\u30ec\u30e0\u30cb\u30b9\u30b1\u30fc\u30c8\u7a4d\u5206\u306b\u95a2\u3057\u3066\uff0c
\n\\[ \\int_{0}^{r} \\frac{dx}{\\sqrt{1-x^4}}=2\\int_{0}^{u} \\frac{dx}{\\sqrt{1-x^4}} \\]
\n\u306e\u3068\u304d
\n\\[ r=\\frac{2u\\sqrt{1-u^4}}{1+u^4} \\]
\n\u304c\u6210\u308a\u7acb\u3064\u3068\u3044\u3046Fagnano\u306e\u767a\u898b\u306b\u623b\u308b\u3002
\n\u3053\u308c\u304c\u500d\u89d2\u516c\u5f0f\u3067\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\uff0c\u4e09\u89d2\u95a2\u6570\u3068\u306e\u30a2\u30ca\u30ed\u30b8\u30fc\u3092\u8003\u3048\u308b\u3068\u826f\u3044\u3002
\n$\\int_{0}^{x} \\frac{dx}{\\sqrt{1-x^2}}=\\arcsin x$
\n\u304c\u6b63\u5f26\u95a2\u6570\u306e\u9006\u95a2\u6570\u3067\u3042\u308b\u3053\u3068\u304b\u3089\uff0c
\n\\[ a=\\int_{0}^{r}\\frac{dx}{\\sqrt{1-x^2}}, \\qquad b=\\int_{0}^{u}\\frac{dx}{\\sqrt{1-x^2}} \\]
\n\u3068\u304a\u304f\u3068\uff0c$r=\\sin a$, $u=\\sin b$ \u3067\u3042\u308b\u3002
\n\\[ \\int_{0}^{r}\\frac{dx}{\\sqrt{1-x^2}}=2\\int_{0}^{u}\\frac{dx}{\\sqrt{1-x^2}} \\]
\n\u306e\u3068\u304d\u306f\uff0c$a=2b$ \u3068\u306a\u308b\u304b\u3089\uff0c
\n\\[ r=\\sin a=\\sin 2b=2\\sin b\\cos b=2u\\sqrt{1-u^2} \\]
\n\u3068\u306a\u308b\u3002<\/p>\n

\u4ee5\u4e0a\u304b\u3089\uff0c
\n\\[ \\int_{0}^{r}\\frac{dx}{\\sqrt{1-x^2}}=2\\int_{0}^{u}\\frac{dx}{\\sqrt{1-x^2}} \\]
\n\u306e\u3068\u304d\u306b\u306f
\n\\[ r=2u\\sqrt{1-u^2} \\]
\n\u304c\u6210\u308a\u7acb\u3064\u304c\uff0c\u3053\u306e\u4e8b\u5b9f\u306f\u6b63\u5f26\u95a2\u6570\u306b\u3064\u3044\u3066\u306e\u500d\u89d2\u516c\u5f0f\u3068\u540c\u3058\u5185\u5bb9\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002
\n<\/latex><\/p>\n","protected":false},"excerpt":{"rendered":"

\u30ec\u30e0\u30cb\u30b9\u30b1\u30fc\u30c8\u306e\u7a4d\u5206 $\\int \\frac{dx}{\\sqrt{1-x^4}}$ \u306e\u3088\u3046\u306b\uff0c3\u6b21\u5f0f\uff0c4\u6b21\u5f0f\u306e\u5e73\u65b9\u6839\u3092\u542b\u3080\u7a4d\u5206\u306f\uff0c \u7dcf\u79f0\u3057\u3066\u6955\u5186\u7a4d\u5206\u3068\u547c\u3070\u308c\u308b\u3002 \u6955\u5186\u306e\u5f27\u9577\u304c\u3053\u306e\u30bf\u30a4\u30d7\u306e\u7a4d\u5206\u306b\u306a\u308b\u3053\u3068\u304c\u540d\u524d\u306e\u7531\u6765\u3067\u3042\u308b\u304c […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-101","post","type-post","status-publish","format-standard","hentry","category-5"],"_links":{"self":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts\/101","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/comments?post=101"}],"version-history":[{"count":0,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts\/101\/revisions"}],"wp:attachment":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/media?parent=101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/categories?post=101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/tags?post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}