从一道例题看积分中值定理的应用

Application of Mean Value Theorem of Integral from an Example

摘要: 积分中值定理是积分学中的最基本理论和性质之一，无论在极限的计算还是积分的计算中都起着至关重要的作用，但是在实际应用中，往往由于对其由来的理解不够全面和深刻而导致用错、算错的情况出现。本文通过一道常见例题的求解来剖析一元函数积分中值定理的应用过程中需要注意和关注的问题。

Abstract: The mean value theorem of integral is one of the most basic theories and properties in Integral calculus. It plays a vital role in both limit calculation and integral calculation. However, in practical application, it is often misused and miscalculated because the understanding of its origin is not comprehensive and profound. This paper analyzes the problems which need to pay attention in the application of the mean value theorem of integral for the functions of one variable, by the process of solving a common example.