{"id":342,"date":"2012-03-24T20:32:42","date_gmt":"2012-03-24T11:32:42","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=342"},"modified":"2021-10-20T19:34:29","modified_gmt":"2021-10-20T10:34:29","slug":"ykr200804","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr200804\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2008\uff1a\u7b2c4\u554f"},"content":{"rendered":"<hr \/>\n<p>\u9023\u7acb\u4e0d\u7b49\u5f0f\r\n\\[\r\n\\left\\{\\begin{array}{l} x^2 +\\left( y -\\dfrac{1}{2} \\right)^2 \\leqq 1 \\\\ y \\geqq 0 \\end{array}\\right.\r\n\\]\r\n\u306e\u8868\u3059\u56f3\u5f62\u3092 \\(x\\) \u8ef8\u306e\u307e\u308f\u308a\u306b\u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u56de\u8ee2\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u4e0e\u3048\u3089\u308c\u305f\u9023\u7acb\u4e0d\u7b49\u5f0f\u306e\u793a\u3059\u9818\u57df\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/yokokoku_r_2008_05_01.png\" alt=\"yokokoku_r_2008_05_01\" class=\"aligncenter size-full\" \/>\r\n\u3053\u308c\u306f, \\(y\\) \u8ef8\u306b\u3064\u3044\u3066\u5bfe\u79f0\u3067\u3042\u308b.<br \/>\r\n\u307e\u305f, \u5186\u5468\u90e8\u5206\u306b\u3064\u3044\u3066<\/p>\r\n<ul>\r\n<li><p>\\(y \\geqq \\dfrac{1}{2}\\) \u306e\u90e8\u5206\u306f, \\(y =\\dfrac{1}{2} +\\sqrt{1-x^2}\\)<\/p><\/li>\r\n<li><p>\\(y \\lt \\dfrac{1}{2}\\) \u306e\u90e8\u5206\u306f, \\(y =\\dfrac{1}{2} -\\sqrt{1-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 _ 0^1 \\left( \\dfrac{1}{2} +\\sqrt{1-x^2} \\right)^2 dx -2\\pi \\displaystyle\\int _ {\\frac{\\sqrt{3}}{2}}^1 \\left( \\dfrac{1}{2} -\\sqrt{1-x^2} \\right)^2 dx \\\\\r\n& = 2\\pi \\displaystyle\\int _ 0^1 \\left( \\dfrac{5}{4} -x^2 +\\sqrt{1-x^2} \\right) dx -2\\pi \\displaystyle\\int _ {\\frac{\\sqrt{3}}{2}}^1 \\left( \\dfrac{5}{4} -x^2 -\\sqrt{1-x^2} \\right) dx \\\\\r\n& = 2\\pi \\displaystyle\\int _ 0^{\\frac{\\sqrt{3}}{2}} \\left( \\dfrac{5}{4} -x^2 \\right) dx +2\\pi \\underline{\\displaystyle\\int _ 0^1 \\sqrt{1-x^2} dx} _ {[1]} +2\\pi \\underline{\\displaystyle\\int _ {\\frac{\\sqrt{3}}{2}}^1 \\sqrt{1-x^2} dx} _ {[2]}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, [1] [2] \u305d\u308c\u305e\u308c\u304c\u4e0b\u56f3\u659c\u7dda\u90e8\u306e\u9762\u7a4d\u3092\u793a\u3059\u3053\u3068\u3092\u5229\u7528\u3059\u308c\u3070<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/yokokoku_r_2008_05_02.png\" alt=\"yokokoku_r_2008_05_02\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\\begin{align}\r\nV & = 2\\pi \\left[ \\dfrac{5x}{4} -\\dfrac{x^3}{3} \\right] _ 0^{\\frac{\\sqrt{3}}{2}} +2\\pi \\cdot \\dfrac{\\pi}{4} +2\\pi \\left( \\dfrac{1}{2} \\cdot 1^2 \\cdot \\dfrac{\\pi}{6} -\\dfrac{1}{2} \\cdot \\dfrac{\\sqrt{3}}{2} \\cdot \\dfrac{1}{2} \\right) \\\\\r\n& = \\sqrt{3} \\pi \\left( \\dfrac{5}{4} -\\dfrac{1}{4} \\right) +\\dfrac{\\pi^2}{2} +\\dfrac{\\pi^2}{6} -\\dfrac{\\sqrt{3} \\pi}{4} \\\\\r\n& =\\underline{\\dfrac{3 \\sqrt{3} \\pi}{4} +\\dfrac{2 \\pi^2}{3}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u9023\u7acb\u4e0d\u7b49\u5f0f \\[ \\left\\{\\begin{array}{l} x^2 +\\left( y -\\dfrac{1}{2} \\right)^2 \\leqq 1 \\\\ y \\geqq 0 \\end{array}\\right. &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/ykr200804\/\">\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":[56],"tags":[16,9],"class_list":["post-342","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2008","tag-16","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/342","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=342"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/342\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=342"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=342"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}