| 定积分换元法的表述 |
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| 引用本文： | 杨合俊. 定积分换元法的表述[J]. 大学数学, 2012, 0(1): 185-191 |
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| 作者姓名： | 杨合俊 |
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| 作者单位： | 长安大学理学院 |
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| 摘 要： | 就定积分换元法的表述,查阅了大量的教科书,并把它们分为六类.通过分析和举反例的方法,发现某些表述中有不必要的条件,某些表述甚至是错误的,而同济大学五版的《高等数学》中的表述更适合于工科学生.
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| 关 键 词： | 定积分 换元法 换元函数 单调性 值域 黎曼可积 |
The Expression of the Substitute Method for Definite Integral |
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| YANG He-jun. The Expression of the Substitute Method for Definite Integral[J]. College Mathematics, 2012, 0(1): 185-191 |
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| Authors: | YANG He-jun |
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| Affiliation: | YANG He-jun(School of Science,Chang’an University,Xi’an 710064,Shaanxi,China) |
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| Abstract: | This paper looked up the expression of the substitute method for definite integral in a large number of textbooks,and divided them into six categories.By analysis methods and give counter-examples,found that some statements in unnecessary conditions,and certain statements are even wrong.The expression in Tongji University,〈Advanced Mathematics〉(5th Edition) is more suitable for engineering students. |
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| Keywords: | definite integral substitute method substitute function monotonicity value range Riemann integral |
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