含积分式方程的解的研究  

Solutions to Integral Equations

作　　者：李高[1] LI Gao(School of Mathematics and Computer Science,Shanxi Datong University,Datong,Shanxi 0370031,China)

机构地区：[1]大同大学数学与计算机科学学院,山西大同037007

出　　处：《河北北方学院学报（自然科学版）》2021年第1期1-3,共3页Journal of Hebei North University:Natural Science Edition

基　　金：山西大同大学教学改革资金资助项目(XJY2013211)。

摘　　要：目的探寻对含有积分式的方程求解的方法。方法利用定积分的存在性,若函数在某闭区间上定积分式存在,则必为一常数,其导数为零。以及积分上限函数是被积函数的原函数这一理论对方程进行取积分或求导。结果若方程只含有定积分,则①方程可以直接求导可求得解;②直接取定积分,可把定积分求得,从而解得方程。若方程含有积分变限函数,则方程可以直接求导可求得解。结论从定积分概念及其积分变限函数的特性入手,逐一进行探索寻觅解决问题的思维方式和思路,并给出解决的方法。Objective The method of solving the equation of integral equation is explored.Methods By using the existence of definite integral,if the integral exists on a closed interval,it must be a constant and its derivative is zero.And the integral upper limit function is the integral of the integral function of the integral function.Results If the equation contains only definite integrals,the equation can be obtained by taking the derivative directly.The definite integral can be obtained by the definite integral and the equation is solved.If the equation contains the integral variable limit function,the equation can be derivative.Conclusion The concept of definite integral and the characteristic of the integral variable limit function are discussed.And the way to solve the problem is explored and the solution is given.

关 键 词：积分式 定积分 求导 变限函数 积分方程 

分 类 号：O017[理学]