翻訳と辞書 Words near each other ・ Sum of absolute transformed differences ・ Sum of angles of a triangle ・ Sum of Christianity ・ Sum of Logic ・ Sum of normally distributed random variables ・ Sum of Parts ・ Sum of perpetuities method ・ Sum of public power ・ Sum of radicals ・ Sum of squares ・ Sum of the Parts ・ Sum of two squares theorem ・ Sum Practysis of Medecyne and other Short Works ・ Sum rule ・ Sum rule in differentiation ・ Sum rule in integration ・ Sum rule in quantum mechanics ・ Sum to Infinity ・ Sum to Infinity (book) ・ Sum Ying Fung ・ Sum-free sequence ・ Sum-free set ・ Sum-frequency generation ・ Sum-of-squares optimization ・ Sum-of-the-parts analysis ・ Sum-product number ・ Sum/One ・ Suma ・ Suma (co-operative) ・ Suma (moth) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sum rule in integration ： ウィキペディア英語版 Sum rule in integration In calculus, the sum rule in integration states that the integral of a sum of two functions is equal to the sum of their integrals. It is of particular use for the integration of sums, and is one part of the linearity of integration. As with many properties of integrals in calculus, the sum rule applies both to definite integrals and indefinite integrals. For indefinite integrals, the sum rule states :$\backslash int\; \backslash left(f\; +\; g\backslash right)\; \backslash ,dx\; =\; \backslash int\; f\; \backslash ,dx\; +\; \backslash int\; g\; \backslash ,dx$ ==Application to indefinite integrals== For example, if you know that the integral of exp(x) is exp(x) from calculus with exponentials and that the integral of cos(x) is sin(x) from calculus with trigonometry then: :$\backslash int\; \backslash left(e^x\; +\; \backslash cos\backslash right)\; \backslash ,dx\; =\; \backslash int\; e^x\; \backslash ,dx\; +\; \backslash int\; \backslash cos\backslash \; \backslash ,dx\; =\; e^x\; +\; \backslash sin\; +\; C$ Some other general results come from this rule. For example: The proof above relied on the special case of the constant factor rule in integration with k=-1. Thus, the sum rule might be written as: :$\backslash int\; (u\; \backslash pm\; v)\; \backslash ,dx\; =\; \backslash int\; u\backslash ,\; dx\; \backslash pm\; \backslash int\; v\backslash ,\; dx$ Another basic application is that sigma and integral signs can be changed around. That is: :$\backslash int\; \backslash sum^b\_\; f\backslash left(r,x\backslash right)\backslash ,\; dx\; =\; \backslash sum^b\_\; \backslash int\; f\backslash left(r,x\backslash right)\; \backslash ,dx$ This is simply because: :$\backslash int\; \backslash sum^b\_\; f(r,x)\backslash ,\; dx$ :$=\; \backslash int\; f\backslash left(a,x\backslash right)\; +\; f((a+1),x)\; +\; f((a+2),x)\; +\; \backslash dots$ ::::::$+\; f((b-1),x)\; +\; f(b,x)\backslash ,\; dx$ :$=\; \backslash int\; f(a,x)\backslash ,dx\; +\; \backslash int\; f((a+1),x)\backslash ,\; dx\; +\; \backslash int\; f((a+2),x)\; \backslash ,dx\; +\; \backslash dots$ ::::::$+\; \backslash int\; f((b-1),x)\backslash ,\; dx\; +\; \backslash int\; f(b,x)\backslash ,\; dx$ :$=\; \backslash sum^b\_\; \backslash int\; f(r,x)\backslash ,\; dx$ 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「Sum rule in 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.