| 简化形式的积分中值定理另一种表述 |
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| 引用本文： | 张乐成,刘学佳,马跃.简化形式的积分中值定理另一种表述[J].大学数学,2009,25(3). |
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| 作者姓名： | 张乐成 刘学佳 马跃 |
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| 作者单位： | 辽宁中医药大学,职业技术学院,数理计算机教研室,辽宁,沈阳,110101 |
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| 摘 要： | 阐述了简化形式的积分中值定理中f(x)不要求连续的情况下成立的条件.即"设函数f(x)在闭区间a,b]上可积,同时f(x)在a,b]上有原函数,则存在ξ∈(a,b),使∫ from x=a to b f(x)dx=f(ξ)(b-a)成立",并且给出了简洁的证明.
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| 关 键 词： | 积分中值定理 不连续 原函数 |
Another Indication of the Simplified Form of Mean Value Theorem for the Integrals |
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| ZHANG Le-cheng,LIU Xue-jia,MA Yue.Another Indication of the Simplified Form of Mean Value Theorem for the Integrals[J].College Mathematics,2009,25(3). |
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| Authors: | ZHANG Le-cheng LIU Xue-jia MA Yue |
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| Institution: | Higher Mathematics office;Liaoning Traditional Chinese Medicine CollegeProfessional and Technological Institute;Liaoning Shengyang 110101;China |
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| Abstract: | Narrating the condition in which f(x) in the simplified form of mean value theorem for the integrals is tenable in discontinuous situation,that's to say,"if function f(x) is possible to be integral on close interval ,and f(x) has the primary function on at the same time,ξ∈(a,b) and ∫ from x=a to b f(x)dx=f(ξ)(b-a) is tenable".The above is proved succinctly. |
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| Keywords: | mean value theorem for the integrals discontinuous primary function |
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