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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 linearity of integration ： ウィキペディア英語版 linearity of integration In calculus, the integral of any linear combination of functions equals the same linear combination of the integrals of the functions; this property is known as linearity of integration.〔.〕 It is a fundamental property of the integral that encapsulates in a single rule two simpler rules of integration, the sum rule (the integral of the sum of two functions equals the sum of the integrals) and the constant factor rule (the integral of a constant multiple of a function equals a constant multiple of the integral).〔.〕 Linearity of integration is related to the linearity of summation, since integrals are thought of as infinite sums. ==Statement and derivation== Let and be functions. Now consider: :$\backslash int\; (af(x)+bg(x))\backslash ,\; dx.$ By the sum rule in integration, this is :$\backslash int\; af(x)\backslash ,\; dx+\backslash int\; bg(x)\backslash ,\; dx.$ By the constant factor rule in integration, this reduces to :$a\backslash int\; f(x)\backslash ,\; dx+b\backslash int\; g(x)\backslash ,\; dx.$ Hence we have :$\backslash int\; (af(x)+bg(x))\backslash ,\; dx=a\backslash int\; f(x)\backslash ,\; dx+b\backslash int\; g(x)\backslash ,\; dx.$ It is also possible to infer linearity of integration as a consequence of linearity of differentiation.〔.〕 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「linearity of integration」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.