积分中值定理的推广与应用系别数学系专业数学与应用数学姓名韩凤指导教师张润玲职称副教授日期2011 年 6 月学校代码10812分 类 号学号107国内图书分类号：吕梁学院本科毕业论文（设计）积分中值定理的推广与应用姓名韩凤系别数学系专业数学与应用数学申请学位学士学位指导教师张润玲职称副教授日期2011 年 6 月摘要在微积分学中积分中值定理与微分中值定理一样有着重要的地位.微积分的许多问题和不等式的证明都以它为依据,积分中值定理在证明有关中值问题时具有极其重要的作用 .它是《数学分析》、《高等数学》课程中定积分部分的基本定理之一.众所周知积分中值定理包括积分第一中值定理与积分第二中值定理,而在数学分析课本上已有过这两个定理的详细证明 ,但这两个定理的推广与应用尚未提及.因此 ,在教学过程中 ,学在运用这一知识点解决有关的数学问题比较困难,常常不知如何下手 ,本文主要讲述的是积分第一中值定理的各种形式的推广以及通过以下几方面的列举例题,加以归纳总结 ,并充分体现积分中值定理在学习解题练习中的应用.关键词：积分中值定理；推广；应用ABSTRACTThe integral median value theorem and differential median value theorem has the same important position in the questions and the proof of the inequality are all based on the integral theorem,the integral median theorem has played an important role in solving the problems about is one of the basic theorems in the definite integral part of “the mathematical analysis”and“the higher mathematics ”.Well-known that the integral median theorem include the first median theorem for integrals and the second median theorem for integrals and the textbooks of the mathematical analysis have the detailed proof about the two theorems,but the popularization and application of the two theorems have not been addressed .Therefore,it is difficult when students use this knowledge to solve the related problems during the process of article mainly introduce various popularization of the first median theorem for integrals and giving some example th...
