| 关于一个积分不等式的证明 |
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| 引用本文： | 刘玲,苏农.关于一个积分不等式的证明[J].数学学习,2010(6):45-46. |
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| 作者姓名： | 刘玲 苏农 |
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| 作者单位： | 北京信息科技大学理学院数学系,北京 100192 |
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| 基金项目： | 基金项目：北京信息科技大学教改项目： 北京信息科技大学投科研基金（102521）. |
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| 摘 要： | 分别利用定积分的定义、Cauchy中值定理、积分变限函数、参数法以及二重积分等证明积分不等式∫01f2(x)dx≥∫01f(x)dx2,其中f(x)在闭区间0,1]上连续.同时归纳出证明积分不等式的几种典型方法.
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| 关 键 词： | 积分不等式 中值定理 积分变限函数 二重积分 |
On Proofs of an Integral Inequality |
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| LIU Ling,SU Nong.On Proofs of an Integral Inequality[J].Studies In College Mathematics,2010(6):45-46. |
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| Authors: | LIU Ling SU Nong |
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| Institution: | (Department of Mathematics, Beijing Information Science and Technology University, Beijing, 100192, PRC) |
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| Abstract: | Several proofs of the integral inequality are presented, where f（x） is continuous on the closed interval 10, 1_1. tAur approacnes are based on the following different viewpoints and methods： definition of a definite integral, Differential Mean Value Theorem, integration as a function of its upper limit, parametric method, and double integral, etc. |
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| Keywords: | integral inequality Differential Mean Value Theorem integration as a function of its limit（s） double integral |
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