摘要
积分中值定理是微积分中的重要内容之一.传统的积分中值定理是建立在定积分的概念上,而对反常积分很少涉及.文中从对无穷区间上连续函数的性质分析出发,建立和证明了无穷区间反常积分的中值定理.它是对反常积分理论和教学方面的有力补充.
The integral mean value theorem is one of the most important contents in calculus.The traditional integral mean value theorem is based on the concept of definite integral,while the improper integral is rarely involved.In this paper,through the analysis of the properties of continuous function on infinite interval,the mean value theorem for improper integral of infinite interval is established and proved.Furthermore,an application example is given to illustrate the conclusion.It is a powerful complement to the improper integral theory.
作者
尚云
邢建民
SHANG Yun;XING Jian-min(College of Mathematics and Physics of Qingdao University of Science and Technical,Qingdao Shandong 266061,China)
出处
《大学数学》
2020年第1期95-99,共5页
College Mathematics
基金
山东省本科高校教学改革重点研究项目(Z2016Z005)。
关键词
无穷限积分
反常积分
积分中值定理
integral of infinite interval
improper integral
mean value theorem for integral
