| 一个积分不等式 |
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| 引用本文： | 胡铭. 一个积分不等式[J]. 高等数学研究, 2013, 0(6): 59-59 |
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| 作者姓名： | 胡铭 |
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| 作者单位： | 武汉科技大学理学院,湖北武汉430065 |
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| 摘 要： | 由连续单调函数的几何意义直观地得出一个不等式，即若设函数f（x）在[0，b]上连续且单调递减，则有b∫0^af（x）dx≥a∫0^bf（x）dx（0≤a≤b）.通过构造辅助函数给出其数学证明，并对其加以推广．
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| 关 键 词： | 连续单调函数 几何意义 积分不等式 |
An Integral Inequality |
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| HU Ming. An Integral Inequality[J]. Studies In College Mathematics, 2013, 0(6): 59-59 |
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| Authors: | HU Ming |
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| Affiliation: | HU Ming (School of Science, Wuhan University of Science and Technology, Wuhan 430065, PRC) |
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| Abstract: | Inspired by its geometric obvio＇us, the integral inequalityb∫0^af（x）dx≥a∫0^bf（x）dx（0≤a≤b）.where f（x） is continuous and monotone decreasing on the interval [0, b], is provedby constructing a proper auxiliary function. |
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| Keywords: | continuous and monotone decreasing function geometric view integral inequality |
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