积分中值定理逆定理的研究

摘要

本文讨论积分中值定理是否具有逆定理,即函数f（x）在[a,b]上连续,对（a,b）内的任意值c,是否存在一个区间[α,β][a,b],使∫αβf（x）dx=f（c）（β-α）。文中对值c分三种情况给出相应的结论.%This paper discusses the integral mean value theorem has a theorem of inverse,that is Function f(x) is continuous in [a,b], (a,b) within an arbitrary value c,Whether there is an interval[α,β][a,b],so that ∫βαf(x)dx=f(c)(β-α) . The conclusion is given in three cases the value c.