{"id":940,"date":"2013-09-20T22:54:52","date_gmt":"2013-09-20T13:54:52","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=940"},"modified":"2021-10-23T03:21:39","modified_gmt":"2021-10-22T18:21:39","slug":"wsr201304","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201304\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52013\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u534a\u5f84 \\(1\\) \u306e\u534a\u5186\u3092\u5e95\u9762\u3068\u3057, \u9ad8\u3055\u304c \\(1\\) \u306e\u534a\u5186\u67f1\u306b\u542b\u307e\u308c\u308b\u7acb\u4f53 \\(R\\) \u304c\u3042\u308b.\r\n\u305d\u306e\u9ad8\u3055 \\(x \\ ( 0 \\leqq x \\leqq 1 )\\) \u3067\u306e\u65ad\u9762\u304c, \u6b21\u306e\u56f3\u306e\u3088\u3046\u306b \\(2\\) \u3064\u306e\u76f4\u89d2\u4e09\u89d2\u5f62\u3092\u5408\u308f\u305b\u305f\u5f62\u306b\u306a\u3063\u3066\u3044\u308b. \u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n\"waseda_r_2013_04_01\"\r\n

    \r\n

  1. (1)<\/strong>\u3000\u9ad8\u3055 \\(x\\) \u3067\u306e \\(R\\) \u306e\u65ad\u9762\u7a4d \\(S(x)\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(R\\) \u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088. \u5fc5\u8981\u306a\u3089\u3070, \u7a4d\u5206\u3059\u308b\u969b\u306b \\(x = \\sin t\\) \u3068\u7f6e\u304d\u63db\u3048\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \u4e0a\u56f3\u306e\u3088\u3046\u306b\u70b9\u3092\u5b9a\u3081\u308b.
    \r\n\u25b3OHP \u306b\u7740\u76ee\u3059\u308b\u3068\r\n\\[\r\n\\text{PH} = \\sqrt{1-x^2}\r\n\\]\r\n\\(\\triangle \\text{AHP} \\sim \\triangle \\text{AOQ}\\) \u3067, \u76f8\u4f3c\u6bd4\u306f \\(1+x : 1\\) \u306a\u306e\u3067\r\n\\[\r\n\\text{OQ} = \\dfrac{\\text{PH}}{1+x} = \\dfrac{\\sqrt{1-x^2}}{1+x}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u9762\u7a4d\u306f\r\n\\[\\begin{align}\r\nS(x) & = 2 \\triangle \\text{ABP} -\\triangle \\text{ABQ} \\\\\r\n& = 2 \\cdot \\dfrac{1}{2} \\cdot 2 \\sqrt{1-x^2} -\\dfrac{1}{2} \\cdot 2 \\cdot \\dfrac{\\sqrt{1-x^2}}{1+x} \\\\\r\n& = \\underline{\\dfrac{( 1+2x ) \\sqrt{1-x^2}}{1+x}}\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    \u6c42\u3081\u308b\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\r\nV = \\displaystyle\\int _ 0^1 S(x) \\, dx\r\n\\]\r\n\u3053\u3053\u3067, \\(x = \\sin t\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{gather}\r\ndx = \\cos t \\, dt , \\\\\r\n\\begin{array}{c|ccc} x & 0 & \\rightarrow & 1 \\\\ \\hline t & 0 & \\rightarrow & \\dfrac{\\pi}{2} \\end{array}\r\n\\end{gather}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nV & = \\displaystyle\\int _ 0^{\\frac{\\pi}{2}} \\dfrac{( 1 +2 \\sin t ) \\cos t}{1 +\\sin t} \\cdot \\cos t \\, dt \\\\\r\n& = \\displaystyle\\int _ 0^{\\frac{\\pi}{2}} \\left( 2 -\\dfrac{1}{1 +\\sin t} \\right) \\cos^2 t \\, dt \\\\\r\n& = \\displaystyle\\int _ 0^{\\frac{\\pi}{2}} \\left\\{ \\cos 2t +1 -( 1 -\\sin t ) \\right\\} \\, dt \\\\\r\n& = \\left[ \\dfrac{1}{2} \\sin 2t -\\cos t \\right] _ 0^{\\frac{\\pi}{2}} \\\\\r\n& = \\underline{1}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u534a\u5f84 \\(1\\) \u306e\u534a\u5186\u3092\u5e95\u9762\u3068\u3057, \u9ad8\u3055\u304c \\(1\\) \u306e\u534a\u5186\u67f1\u306b\u542b\u307e\u308c\u308b\u7acb\u4f53 \\(R\\) \u304c\u3042\u308b. \u305d\u306e\u9ad8\u3055 \\(x \\ ( 0 \\leqq x \\leqq 1 )\\) \u3067\u306e\u65ad\u9762\u304c, \u6b21\u306e\u56f3\u306e\u3088\u3046\u306b \\(2\\) \u3064\u306e … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[100],"tags":[147,111],"class_list":["post-940","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2013","tag-waseda_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/940","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=940"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/940\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=940"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=940"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}