第二积分中值定理的一个非常规证明

An Unconventional Proof of the Second Integral Mean Value Theorem

摘要: 第二积分中值定理是与第一积分中值定理相互独立的一个定理，属于积分中值定理。它可以用来证明Dirichlet-Abel反常Riemann积分判别法。在数学竞赛及考研试题中经常会出现涉及第二积分中值定理的题目。本文我们通过Weierstrass逼近定理，利用Bernstein多项式来证明积分第二中值定理。

Abstract: The second integral mean value theorem is an independent theorem from the first integral mean value theorem, which belongs to the integral mean value theorem. It can be used to prove the Riemann integral criterion for Dirichlet Abel anomaly. In mathematics competition and postgraduate entrance examination, there are often problems related to the second integral mean value theorem. In this paper, we prove the second mean value theorem of integrals by using the Weierstrass approximation theorem and Bernstein polynomials.