探究几类与定积分等式相关的证明问题  

Exploring Several Proof Problems Related to Definite Integral Equation

作　　者：贾瑞玲 文生兰[1] 孙铭娟 

机构地区：[1]信息工程大学,河南 郑州

出　　处：《理论数学》2023年第9期2648-2657,共10页Pure Mathematics

摘　　要：定积分等式是微积分理论的重要组成部分,与微分等式相辅相成。在数学研究中,定积分等式被广泛应用于证明各种数学定理、推导各种数学关系,对于理解数学原理、解决实际问题以及推动科学发展都起着重要的作用。由于其解题理论涉及到微分与积分,且证明方法繁多,这给许多学生带来了学习困难。很多学者对这方面也进行了相关研究并取得了一定的成果。在前人研究的基础上,本文深入剖析与定积分等式相关的三个主要方面,并挖掘解决这些问题的一般方法与思路,同时也对相关问题进行了推广;旨在帮助学生更深入地理解积分理论。Definite integral equation is an important part of calculus theory, which complements differential equation. In mathematical research, definite integral equation is widely used to prove various mathematical theorems and deduce various mathematical relations, which play an important role in understanding mathematical principles, solving practical problems and promoting scientific development. Due to the fact that its problem-solving theory involves differential and integral, and there are many proof methods, it brings learning difficulties to many students. Many scholars have also done relevant research in this field and achieved certain results. On the basis of previous re-search, this paper deeply analyzes three main aspects related to definite integral equation, digs out the general methods and ideas to solve these problems, and popularizes the related problems at the same time. It aims to help students understand the integral theory more deeply.

关 键 词：积分等式 积分中值定理 零点问题 积分变限函数 坏点 

分 类 号：G63[文化科学—教育学]