关于一道典型定积分不等式的演绎  

A Deduction of a Typical Definite Integral Inequality

作　　者：黄新荣 袁达明 HUANG Xinrong;YUAN Daming(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang,Jiangxi,330022,PRC)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022

出　　处：《高等数学研究》2021年第6期32-34,共3页Studies in College Mathematics

基　　金：国家自然科学基金(11861039);江西师范大学教学改革课题(JXSDJG16055).

摘　　要：此文以一道典型定积分不等式证明题为例,深刻分析共证法,并推广到任意有限闭区间上.在推广过程中分别设定被积函数所需要满足的条件,从而得到关于定积分不等式的一般性命题.同时根据所给定积分不等式的证明思路,来启发演绎对于一般性命题的证明.In this paper,we take a typical definite integral inequality as an example,analyze the common dialectics,and extend to any finite closed interval.In the process of generalization,the conditions which the integrand needs to satisfy are set respectively,and the general propositions about the definite integral inequality are obtained.The idea of the proof of the given integral inequality inspires the deduction of the proof of the general proposition.

关 键 词：定积分 不等式 

分 类 号：O13[理学—数学] O178[理学—基础数学]