关于广义积分的若干问题探讨  

Discussion on Some Problems about Generalized Integral

作　　者：牛荟玲 刘佳音 NIU Huiling;LIU Jiayin(North Minzu University,Yinchuan,Ningxia Hui Autonomous Region,750021 China)

机构地区：[1]北方民族大学,宁夏银川750021

出　　处：《科技创新导报》2021年第20期163-166,共4页Science and Technology Innovation Herald

基　　金：北方民族大学教育教学改革研究项目(项目编号:2020YBJY50,2019JY0007)。

摘　　要：广义积分是积分学中的一个重要概念,它是定积分概念的推广,也是定积分无穷多项累加思想的推广。本文首先通过定积分的定义,深入分析了无穷区间上的广义积分以及无界函数的广义积分与定积分之间的区别和联系。其次,讨论了当被积函数的原函数容易求出时,利用广义积分的定义计算广义积分时需要注意的几个问题,并举例加以说明。Generalized integral is an important concept in integral science.It is not only the extension of the concept of def inite integral,but also the extension of the idea of infinite multinomial accumulation of def inite integral.Firstly,through the definition of definite integral,this paper deeply analyzes the differences and relations between generalized integral on infinite interval and generalized integral and definite integral of unbounded function.Secondly,when the or iginal function of the integrand f unction is easy to be obtained,several problems needing attention in calculating the generalized integral by using the def inition of the generalized integral are discussed and illustrated with examples.

关 键 词：广义积分 被积函数 积分区间 定积分 原函数 

分 类 号：O13[理学—数学]