积分中值定理的一点注记及其应用

A Note on the Integral Mean Value Theorem and its Application

积分中值定理是微积分学中一个重要定理,但若被积函数是一个函数列fn(x)时,在应用上往往出错,有时误用该定理.文章通过分析误用积分中值定理求解limn→∞∫π/20sinnxdx,n∈N的例乙子入手,对积分中值定理进行了推广,给出了中值点与无关的推广结论及其应.

Integral mean value theorem is an important theorem in calculus, but if it is a function of the product function, some errors are often used in the application. In this paper, we analyze the examples of the application of the theorem of the mean value of the misuse of the integral.