| 一个积分等式的推广与应用 |
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| 引用本文： | 游雪肖,赵大方.一个积分等式的推广与应用[J].数学学习,2014(1):59-61. |
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| 作者姓名： | 游雪肖 赵大方 |
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| 作者单位： | 湖北师范学院数学与统计学院 |
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| 摘 要： | 从积分限和积分次数两方面推广关系式∫0^xf（t）（x-t）dt=∫0^x（∫0^tf（u）du） dt,其中f（x）为连续函数,并举例说明所得结论在累次积分计算中的应用.
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| 关 键 词： | 定积分 累次积分 分部积分公式 |
Generalization and Application of an Integral Formula |
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| YOU Xuexiao;ZHAO Dafang.Generalization and Application of an Integral Formula[J].Studies In College Mathematics,2014(1):59-61. |
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| Authors: | YOU Xuexiao;ZHAO Dafang |
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| Institution: | YOU Xuexiao;ZHAO Dafang;School of Mathematics and Statistics,Hubei Normal University; |
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| Abstract: | In this paper,the integral formula∫0^x f（t）（x-t）dt=∫0^x（ ∫0^t f（u）du）dt,where fis continuous,is generalized in terms of the limit of integration,and the number of iterations.Five propositions are obtained,and examples of solving iterated integrals are given. |
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| Keywords: | definite integral iterated integral integration by parts |
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