| 积分中值定理的推广及其“中间点”的性质 |
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| 引用本文： | 戴振强.积分中值定理的推广及其“中间点”的性质[J].高师理科学刊,2007,27(4):21-22,25. |
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| 作者姓名： | 戴振强 |
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| 作者单位： | 河源职业技术学院,广东,河源,517000 |
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| 摘 要： | 积分中值定理中将"f(x)在a,b]上连续"改为"f(x)在a,b]上可积",定理的结论仍然成立.据此证明了"中间点"唯一存在的充要条件是被积函数的单调性,还可以在满足李普希兹条件下给出"中间点"的渐近性.
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| 关 键 词： | 黎曼积分中值定理 中间点 渐近性 |
| 文章编号： | 1007-9831（2007）04-0021-03 |
| 收稿时间： | 2007-02-01 |
| 修稿时间： | 2007-02-01 |
On the promotion of integral value theorem and the nature of its middle point |
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| DAI Zhen-qiang.On the promotion of integral value theorem and the nature of its middle point[J].Journal of Science of Teachers＇College and University,2007,27(4):21-22,25. |
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| Authors: | DAI Zhen-qiang |
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| Institution: | Heyuan Vocational Technical College, Heyuan 517000, China |
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| Abstract: | Proved that Integral theorem remains valid if Integral theorem of f(x) can be continued in a,b] is changed into that of f(x) can be producted in a,b].This proved that the only necessary and sufficient existing condition of the middle point is the monotony of producted function,and also meet the conditions Lipschitzienne given the middle point of asymptotic behavior. |
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| Keywords: | Riemann integral value theorem middle point asymptotic behavior |
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