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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Iterated integral ： ウィキペディア英語版 Iterated integral In calculus an iterated integral is the result of applying integrals to a function of more than one variable (for example $f(x,y)$ or $f(x,y,z)$) in a way that each of the integrals considers some of the variables as given constants. For example, the function $f(x,y)$, if $y$ is considered a given parameter can be integrated with respect to $x$, $\backslash int\; f(x,y)dx$. The result is a function of $y$ and therefore its integral can be considered. If this is done, the result is the iterated integral :$\backslash int\backslash left(\backslash int\; f(x,y)\backslash ,dx\backslash right)\backslash ,dy.$ It is key for the notion of iterated integral that this is different, in principle, from the multiple integral :$\backslash iint\; f(x,y)\backslash ,dx\backslash ,dy.$ Although in general these two can be different there is a theorem that, under very mild conditions, gives the equality of the two. This is Fubini's theorem. The alternative notation for iterated integrals :$\backslash int\; dy\; \backslash int\; f(x,y)\backslash ,dx$ is also used. Iterated integrals are computed following the operational order indicated by the parentheses (in the notation that uses them). Starting from the most inner integral outside. ==Examples== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Iterated integral」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.