{"id":9046,"date":"2024-07-03T10:49:37","date_gmt":"2024-07-03T01:49:37","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=9046"},"modified":"2024-07-04T10:44:54","modified_gmt":"2024-07-04T01:44:54","slug":"2%e9%87%8d%e7%a9%8d%e5%88%86%e3%81%ae%e4%be%8b%e9%a1%8c","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/%e5%a4%9a%e9%87%8d%e7%a9%8d%e5%88%86%ef%bc%9a%e5%a4%9a%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e7%a9%8d%e5%88%86\/2%e9%87%8d%e7%a9%8d%e5%88%86\/2%e9%87%8d%e7%a9%8d%e5%88%86%e3%81%ae%e4%be%8b%e9%a1%8c\/","title":{"rendered":"2\u91cd\u7a4d\u5206\u306e\u4f8b\u984c"},"content":{"rendered":"

<\/p>\n

\u4f8b\u984c 1<\/h3>\n

$\\displaystyle \\iint_D x\\, dx\\, dy, \\quad D: 0 \\leq x \\leq 1, \\ 0 \\leq y \\leq 2$<\/p>\n

\u89e3\u7b54\u4f8b<\/h4>\n

\\begin{eqnarray}
\n\\iint_D x\\, dx\\, dy &=& \\int_0^2 dy\\, \\int_0^1 dx\\, x \\\\
\n&=& \\int_0^2 dy\\, \\left[ \\frac{x^2}{2}\\right]_0^1 \\\\
\n&=& \\int_0^2 dy\\, \\frac{1}{2} \\\\
\n&=& \\biggl[\\frac{y}{2} \\biggl]_0^2\\\\
\n&=& 1
\n\\end{eqnarray}<\/p>\n

\u4f8b\u984c 2<\/h3>\n

$\\displaystyle \\iint_D (x + y) \\, dx\\, dy, \\quad D: 0 \\leq x \\leq 1, \\ 0 \\leq y \\leq 2$<\/p>\n

\u89e3\u7b54\u4f8b<\/h4>\n

\\begin{eqnarray}
\n\\iint_D (x + y) \\, dx\\, dy &=& \\iint_D x\\, dx\\, dy + \\iint_D y\\, dx\\, dy \\\\
\n&=& \\int_0^2 dy \\int_0^1 dx\\, x + \\int_0^1 dx \\int_0^2 dy\\, y \\\\
\n&=& \\biggl[\\, y \\,\\biggr]_0^2 \\times \\left[ \\frac{x^2}{2}\\right]_0^1 + \\biggl[\\, x \\,\\biggr]_0^1 \\times \\left[ \\frac{y^2}{2}\\right]_0^2 \\\\
\n&=& 2 \\times \\frac{1}{2} + 1 \\times 2 \\\\
\n&=& 3
\n\\end{eqnarray}<\/p>\n

\u5225\u89e3 1<\/h4>\n

\u3053\u3053\u3067\u306f\u5f8c\u3067\u8aac\u660e\u3059\u308b\u3088\u3046\u306b\u7d2f\u6b21\u7a4d\u5206<\/a><\/strong><\/span>\u306e\u65b9\u6cd5\u3067\u7a4d\u5206\u3057\u3066\u3044\u308b\u30022\u91cd\u7a4d\u5206\u3092\u7d2f\u6b21\u7a4d\u5206\u306e\u65b9\u6cd5\u3067\u8a08\u7b97\u3059\u308b\u969b\uff0c\u5148\u306b $\\displaystyle \\int_0^1 dx\\, (x +\u00a0 y)$ \u306e\u7a4d\u5206\u3092\u3059\u308b\u969b\u306b\u306f\uff0c$x$ \u306e\u307f\u306b\u3064\u3044\u3066\u306e\u7a4d\u5206\u3067\u3042\u308b\u304b\u3089\uff0c$y$ \u306f\u56fa\u5b9a\u3057\u3066\uff0c\u3042\u305f\u304b\u3082\u5b9a\u6570\u306e\u3088\u3046\u306b\u6271\u3063\u3066 $x$ \u306b\u3064\u3044\u3066\u7a4d\u5206\u3059\u308b<\/strong><\/span>\u3002\u3053\u308c\u304c2\u91cd\u7a4d\u5206\u3092\u7d2f\u6b21\u7a4d\u5206\u306e\u65b9\u6cd5\u3067\u8a08\u7b97\u3059\u308b\u3068\u304d\u306e\u3084\u308a\u304b\u305f\u3002\u7d2f\u6b21\u7a4d\u5206\u306e\u8aac\u660e\u3092\u805e\u3044\u305f\u3042\u3068\u306b\uff0c\u3042\u3089\u305f\u3081\u3066\u3058\u3063\u304f\u308a\u8a08\u7b97\u3057\u3066\u307f\u3088\u3046\u3002<\/p>\n

\\begin{eqnarray}
\n\\iint_D (x + y) \\, dx\\, dy
\n&=& \\int_0^2 dy \\int_0^1 dx\\, (x +\u00a0 y) \\\\
\n&=& \\int_0^2 dy \\, \\left[ \\frac{x^2}{2} + y x\\right]_0^1 \\\\
\n&=& \\int_0^2 dy \\, \\left(\\frac{1}{2} + y\\right) \\\\
\n&=& \\left[\\frac{y}{2} + \\frac{y^2}{2} \\right]_0^2 \\\\
\n&=& 1 + 2 \\\\
\n&=& 3
\n\\end{eqnarray}<\/p>\n

\u5225\u89e3 2<\/h4>\n

\\begin{eqnarray}
\n\\iint_D (x + y) \\, dx\\, dy &=& \\int_0^1 dx \\int_0^2 dy \\, (x +\u00a0 y) \\\\
\n&=& \\cdots
\n\\end{eqnarray}<\/p>\n

\u3053\u308c\u306f\u30c0\u30e1<\/h4>\n

\u4f8b\u984c 1 \u306f\u72ec\u7acb\u3057\u305f\u7a4d\u5206\u306e\u639b\u3051\u7b97\u3068\u306a\u3063\u305f\u306e\u3067\uff0c\u3053\u306e\u554f\u984c\u3082<\/p>\n

\\begin{eqnarray}
\n\\iint_D (x + y) \\, dx\\, dy
\n&=& \\int_0^2 dy \\int_0^1 dx\\, (x +\u00a0 y) \\\\
\n&=& \\left\\{\\int_0^2 dy \\right\\}\u00a0 \\times \\int_0^1 dx\\, (x +\u00a0 y) \\\\
\n&=& 2 \\times\\int_0^1 dx\\, (x +\u00a0 y)
\n\\end{eqnarray}<\/p>\n

\u306e\u3088\u3046\u306b $y$ \u7a4d\u5206\u3092\u5148\u306b\u8a08\u7b97\u3057\u3066\u639b\u3051\u7b97\u3068\u3057\u3066\u3044\u3044\u3067\u3059\u304b\u3041\uff1f<\/strong><\/span>\u3068\u3044\u3046\u8cea\u554f\u304c\u3042\u3063\u305f\u306e\u3067\uff0c\u305d\u308c\u306f\u30c0\u30e1<\/strong><\/span>\u3002<\/p>\n

\u3088\u304b\u308c\u3068\u601d\u3063\u3066\u3061\u3087\u3063\u3068\u30de\u30cb\u30a2\u30c3\u30af\u306a\u8868\u8a18\u6cd5\u3092\u4f7f\u3046\u3068\u3053\u3093\u306a\u52d8\u9055\u3044\u3092\u3059\u308b\u306e\u3067\uff0c\u3061\u3083\u3093\u3068\u66f8\u304f\u3068<\/p>\n

\\begin{eqnarray}
\n\\iint_D (x + y) \\, dx\\, dy
\n&=& \\int_0^2 \\left\\{ \\int_0^1 (x +\u00a0 y) \\,dx\\,\\right\\}\\, dy
\n\\end{eqnarray}<\/p>\n

\u3053\u306e\u3088\u3046\u306b\u66f8\u304f\u3068\uff0c$\\int$ \u3068 $dy$ \u306e\u9593\u306b\u88ab\u7a4d\u5206\u95a2\u6570<\/strong><\/span>\u304c\u3042\u308b\u304b\u3089\uff0c$\\displaystyle \\int_0^2 dy = 2$ \u3092\u5148\u306b\u8a08\u7b97\u3059\u308b\u306a\u3069\u3068\u3044\u3046\u3053\u3068\u306f\u601d\u3044\u6d6e\u304b\u3070\u306a\u3044\u3067\u3057\u3087\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":2330,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-9046","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t