广义的变限积分函数求导公式证明及其应用  

Proof of the Derivation Formula of Generalized Variable Limit Integral Function and Its Application

作　　者：王瑞星 徐清华 刘烁 吴克坚 WANG Ruixing;XU Qinghua;LIU Shuo;WU Kejian(School of Basic Medicine, Air Force Medical University, Xi′an 710032, China)

机构地区：[1]空军军医大学基础医学院,陕西西安710032

出　　处：《河南教育学院学报（自然科学版）》2022年第2期60-66,共7页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：空军军医大学基础医学院“人才建设行动计划”公共教研室骨干人才项目。

摘　　要：针对高等数学中学生不太容易理解的变限积分函数的求导问题,首先分析了变限积分函数的本质及其重要意义所在,然后给出了更为一般化的广义的变限积分函数求导公式、广义的含参变量的变限积分函数求导公式,并基于导数的定义给出了两个求导公式的证明过程。通过对广义的变限积分函数求导公式的推导以及对历年竞赛、考研相关题目的分析,使学生更加清楚学习变限积分函数的目的、更加灵活地应用广义的变限积分函数的求导方法。Aiming at the derivation problem of variable limit integral function which is not easy to understand for students in higher mathematics,first analyzed the essence and significance of variable limit integral function,and then gave a more general derivative formula of generalized variable limit integral function and a generalized derivative formula of variable limit integral function with parameter variable.Based on the definition of derivative,the proof of two derivation formulas was given.Through the derivation of the derivative formula of the generalized variable limit integral function and the analysis of the related topics of mathematics competition and postgraduate entrance examination over the years,students can learn the original intention of the variable limit integral function more clearly and apply the derivative method of the generalized variable limit integral function more flexibly.

关 键 词：广义的变限积分函数 求导公式 积分中值定理 导数的定义 参变量 

分 类 号：G642.0[文化科学—高等教育学]