{"id":411,"date":"2012-05-27T21:16:00","date_gmt":"2012-05-27T12:16:00","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=411"},"modified":"2021-10-23T03:48:24","modified_gmt":"2021-10-22T18:48:24","slug":"wsr201205","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201205\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52012\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(xy\\) \u5e73\u9762\u4e0a\u306b \\(2\\) \u70b9 A \\((-1,0)\\) , B \\((1,0)\\) \u3092\u3068\u308b.\r\n\\(\\dfrac{\\pi}{4} \\leqq \\angle \\text{APB} \\leqq \\pi\\) \u3092\u307f\u305f\u3059\u5e73\u9762\u4e0a\u306e\u70b9 P \u306e\u5168\u4f53\u3068\u70b9 A , B \u304b\u3089\u306a\u308b\u56f3\u5f62\u3092 \\(F\\) \u3068\u3059\u308b. \u3064\u304e\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(F\\) \u3092\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(F\\) \u3092 \\(x\\) \u8ef8\u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3057\u3066\u5f97\u3089\u308c\u308b\u7acb\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u5186\u5468\u89d2\u306e\u5b9a\u7406\u3088\u308a, \\(\\angle \\text{ACB} =\\dfrac{\\pi}{2}\\) \u3068\u306a\u308b\u70b9 C \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u5186\u306e\u5185\u90e8\u307e\u305f\u306f\u5468\u306e\u3046\u3061, AB \u306b\u5206\u3051\u3089\u308c\u308b\u90e8\u5206\u306e\u70b9 C \u3092\u542b\u3080\u90e8\u5206\u304c\u6761\u4ef6\u3092\u307f\u305f\u3059.<br \/>\r\n\u70b9 C \u306e\u5019\u88dc\u306f\u70b9 \\((0, \\pm 1)\\) \u306e \\(2\\) \u70b9\u3042\u308b.<br \/>\r\n\u3088\u3063\u3066, \\(F\\) \u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u3092\u542b\u3080\uff09.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/waseda_r_2012_05_01.png\" alt=\"waseda_r_2012_05_01\" class=\"aligncenter size-full\" \/>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u5bfe\u79f0\u6027\u3088\u308a, \\(x \\geqq 0 , \\, y \\geqq 0\\) \u306e\u90e8\u5206\u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.<br \/>\r\n\u5883\u754c\u90e8\u5206\u306e\u65b9\u7a0b\u5f0f\u306f<\/p>\r\n<ul>\r\n<li><p>\\(y \\geqq 1\\) \u306e\u90e8\u5206 : \\(y _ {+} = 1 +\\sqrt{2-x^2}\\)<\/p><\/li>\r\n<li><p>\\(y \\lt 1\\) \u306e\u90e8\u5206 : \\(y _ {-} = 1 -\\sqrt{2-x^2}\\)<\/p><\/li>\r\n<\/ul>\r\n<p>\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\\begin{align}\r\nV & =2 \\pi \\displaystyle\\int _ 0^{\\sqrt{2}} {y _ {+}}^2 \\, dx -2 \\pi \\displaystyle\\int _ 1^{\\sqrt{2}} {y _ {-}}^2 \\, dx \\\\\r\n& = 2 \\pi \\displaystyle\\int _ 0^{\\sqrt{2}} \\left( 3-x^2 +2 \\sqrt{2-x^2} \\right) \\, dx \\\\\r\n& \\qquad -2 \\pi \\displaystyle\\int _ 1^{\\sqrt{2}} \\left( 3-x^2 -2 \\sqrt{2-x^2} \\right) \\, dx \\\\\r\n& = 2 \\pi \\displaystyle\\int _ 0^{1} \\left( 3-x^2 \\right) \\, dx +4 \\pi \\underline{\\displaystyle\\int _ 0^{\\sqrt{2}} \\sqrt{2-x^2} \\, dx} _ {[1]} \\\\\r\n& \\qquad +4 \\pi \\underline{\\displaystyle\\int _ 1^{\\sqrt{2}} \\sqrt{2-x^2} \\, dx} _ {[2]}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, [1] [2] \u306f\u305d\u308c\u305e\u308c\u4e0b\u56f3\u306e\u659c\u7dda\u90e8\u306e\u9762\u7a4d\u306a\u306e\u3067<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/waseda_r_2012_05_02.png\" alt=\"waseda_r_2012_05_02\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\\begin{align}\r\n[1] & = \\dfrac{1}{2} \\cdot \\left( \\sqrt{2} \\right)^2 \\cdot \\dfrac{\\pi}{2} = \\dfrac{\\pi}{2} , \\\\\r\n[2] & = \\dfrac{1}{2} \\cdot \\left( \\sqrt{2} \\right)^2 \\cdot \\dfrac{\\pi}{4} +\\dfrac{1}{2} \\cdot 1^2 \\\\\r\n& = \\dfrac{\\pi}{4} +\\dfrac{1}{2}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\nV & = 2 \\pi \\left[ x -\\dfrac{x^3}{3} \\right] _ 0^1 +4 \\pi \\cdot \\dfrac{\\pi}{2} +4 \\pi \\left( \\dfrac{\\pi}{4} +\\dfrac{1}{2} \\right) \\\\\r\n& = \\dfrac{4 \\pi}{3} +2 \\pi^2 +\\pi^2 +2 \\pi \\\\\r\n& = \\underline{\\dfrac{10 \\pi}{3} +3 \\pi^2}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306b \\(2\\) \u70b9 A \\((-1,0)\\) , B \\((1,0)\\) \u3092\u3068\u308b. \\(\\dfrac{\\pi}{4} \\leqq \\angle \\text{APB} \\leqq \\pi\\) \u3092\u307f\u305f\u3059\u5e73 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/wsr201205\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[64],"tags":[147,68],"class_list":["post-411","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2012","tag-waseda_r","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/411","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=411"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/411\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}