函数可积与原函数存在的条件探究  

Study on Conditions of Integrability and Existence of Primitive Functions

作　　者：郝琳 赵志辉 屈娜 陈春梅 HAO Lin;ZHAO Zhihui;QU Na;CHEN Chunmei(Department of Basic Courses,Rocket Force University of Engineering,Xi′an 710025,China)

机构地区：[1]火箭军工程大学基础部,陕西西安710025

出　　处：《河南财政金融学院学报(自然科学版)》2024年第4期51-54,共4页Journal of Henan Finance University(Natural Science Edition)

基　　金：军队院校数学教学研究课题(JY23B016)。

摘　　要：探究了函数可积的充分条件、可积的必要条件、原函数存在的充分条件,证明了具有第一类间断点的函数、具有无穷间断点的函数一定不存在原函数,并指出函数的可积性与原函数存在性之间没有关系.Some conditions are studied such as the sufficient conditions of integrability,the necessary conditions of integrability,and the sufficient conditions of the existence of primitive function.And some functions,with discontinuous point of the first kind or infinite discontinuity,are proved to have no primitive function.And the conclusion points out that there is no relationship between integrability and existence of primitive function.

关 键 词：可积 原函数 第一类间断点 无穷间断点 

分 类 号：O172.2[理学—数学]