用柯西中值定理证明积分中值定理  

Comfirmation of Integral Mean Value Theorem by Cauchy Mean Value Theorem

作　　者：王凡彬[1] 

机构地区：[1]内江师范学院数学与信息科学学院四川省高等学校数值仿真重点实验室,四川内江641100

出　　处：《内江师范学院学报》2010年第12期11-13,16,共4页Journal of Neijiang Normal University

基　　金：内江师范学院重点科研项目(09NJZ-1);四川省高等学校数值仿真重点实验室重点科研项目(09NJZZ001)

摘　　要：为了建立柯西中值定理与积分中值定理两类不同性质的中值定理的关系,利用柯西中值定理证明了积分中值定理.在定积分情形下,利用积分上限函数和柯西中值定理证明了积分中值定理;在重积分情形下,利用积分上限函数、柯西中值定理和区域函数的概念证明了积分中值定理.初步建立了两类不同性质的中值定理的关系.For the aim of making clear the relation lying in between the Cauchy mean value theorem and the integral mean value theorem,the confirmation of integral mean value by Cauchy mean value theorem is carried out.In the case of definite integral,by use of Cauchy Mean Value Theorem and Integral Upper Limit function,integral Mean Value Theorem is proved.In the case of multiple integral,using Cauchy mean value theorem,the concept of integral upper limit function and regional function,integral mean value theorem is also proved.The relation between the two types of mean value theorems was initially established

关 键 词：柯西中值定理 积分中值定理 区域函数 

分 类 号：O172[理学—数学]