关于连续函数的积分第二中值定理的简单证明

A Simple Proof of Second Mean Value Theorem for Integrals with Continuous Functions

三大微分中值定理中,罗尔定理常常被用来证明拉格朗日中值定理和柯西中值定理。文章将借助积分推广的第一中值定理,给出在函数连续条件下积分第二中值定理的简单证明。

In three types of Differential Mean Value Theorem,Rolle theorem can be used to prove Lagrange mean value theorem and Cauchy mean value theorem.In this paper,with the help of the generalized first mean value theorem of integrals,a simple proof of the second mean value theorem of integrals under continuous conditions is given.