关于积分第二中值定理及其应用探究

Second Mean Value Theorem of Integrals and Its Applications

在数学分析中积分中值定理与微分中值定理同样重要,而且应用积分中值定理求解题目的方法和技巧多种多样。文章主要对积分第二中值定理的三种形式加以探究,并通过典型例题指出,适当地作变量替换可将所求解的问题转化为适宜利用积分第二中值定理的情形,从而使问题得以简化求解。

Integral mean value theorem and differential mean value theorem are of equal importance in mathematical analysis, and there are a variety of methods and techniques of applying integral mean value theorem to solving questions. In this paper, we study various forms of second mean value theorem of integrals, some typical examples point out that proper variable substitution can convert the problem to a simple form, which can be easily solved by the second mean value theorem of integrals.