长江大学学报（自科版）2018，Vol.15Issue(9)：72-76,5.
应用黎曼-斯蒂尔杰斯积分证明黎曼第二积分中值定理
Proving the Second Mean Value Theorem for Riemann Integrals by Riemann-Stieltjes Integrals
摘要
Abstract
The second mean value theorem for Riemann integrals is an important result in mathematical analysis with many applications in the theories of improper integrals and series.On the other hand,it is also a difficulty for teaching.In the text book 《 Mathematical Analysis》 published by East China Normal University,the proof of the theorem is quite complicated from which the essential of the proof is covered to a large extent.Proving the second mean value theorem for Riemann integrals by integrating by parts formula of Riemann-Stieltjes integrals is much more simpler,and is easy to be used to prove other results such as the Dirichlet criteria for improper integrals.关键词
黎曼第二积分中值定理/黎曼-斯蒂尔杰斯积分/分部积分Key words
the second mean value theorem of Riemann integrals/Riemann-Stieltjes integrals/integrating by parts分类
数理科学引用本文复制引用
余婷,向长林..应用黎曼-斯蒂尔杰斯积分证明黎曼第二积分中值定理[J].长江大学学报（自科版）,2018,15(9):72-76,5.基金项目
NSFC(11701045) （11701045）
Yangtze Youth Fund (2016cqn56). （2016cqn56）
