[1]赵显曾.关于积分第二中值定理的一个注记[J].东南大学学报(自然科学版),1988,18(5):47-52.[doi:10.3969/j.issn.1001-0505.1988.05.007]
　Zhao Xianzeng (Department of Mathematics and Mechanics).A Note on the Second Mean Value Theorem for Integrals[J].Journal of Southeast University (Natural Science Edition),1988,18(5):47-52.[doi:10.3969/j.issn.1001-0505.1988.05.007]
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关于积分第二中值定理的一个注记()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
18
期数:
1988年第5期
页码:
47-52
栏目:
本刊信息
出版日期:
1988-09-20

文章信息/Info

Title:
A Note on the Second Mean Value Theorem for Integrals
作者:
赵显曾
南京工学院数学力学系
Author(s):
Zhao Xianzeng (Department of Mathematics and Mechanics)
关键词:
积分学;  Riemann积分;  中值定理
Keywords:
integral;  Riemann integrat;  mean-value theorem
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1988.05.007
摘要:
本文在Riemann积分第二中值定理中,加上一个非常一般化的条件后,得出了一个较强的结果:设函数f在区间[a,b]上非负、不增,且f(a+0)-f(b-0)>0,函数g在[a,b]上Riemann可积,则存在一点ξ∈(a,b),使得integral from n=a to b f(x)g(x)dx=f(a)integral from n=a to ξ g(x)dx。
Abstract:
Adding a condition in the second mean-value theorem the author obtains Theorem 3, that is, if f is a nonnegative, monotone decreasing function defined on [a, b] and f(a+0)-f(b-0)>0, g is a Riemann integrable function, then there is a point ξ∈(a, b) that integral from a to b(f(x)g(x)dx=f(a)integral from α to ξ(g(x)dx).

相似文献/References:

[1]赵显曾.关于Riemann可积函数的本性[J].东南大学学报(自然科学版),1995,25(6):9.[doi:10.3969/j.issn.1001-0505.1995.06.002]
　Zhao Xianzeng.On Essential Feature of Kiemann-Integrable Functions[J].Journal of Southeast University (Natural Science Edition),1995,25(5):9.[doi:10.3969/j.issn.1001-0505.1995.06.002]

更新日期/Last Update: 2013-04-30