浅析定积分微元法中微元的选取  

A Brief Analysis on the Selection of Micro-elements in the Definite Integral Element Method

作　　者：张锐 詹紫浪 ZHANG Rui;ZHAN Zi-lang(School of Information Engineering,Lanzhou City University,Lanzhou Gansu 730070;Editorial Department of Journal of Gansu Normal Colleges,Lanzhou Gansu 730070)

机构地区：[1]兰州城市学院信息工程学院,甘肃兰州730070 [2]甘肃高师学报编辑部,甘肃兰州730070

出　　处：《甘肃高师学报》2022年第2期4-6,共3页Journal of Gansu Normal Colleges

基　　金：甘肃省教育科学“十三五”规划2019年度重点课题“新工科背景下地方应用型本科院校高等数学教学改革研究”(GS[2019]GHBZ146).

摘　　要：定积分的微元法对微元的选取不是随意的,而是有一定要求的,如果达不到要求,得到的计算公式就是错误的.文章在强调微元的选取必须遵循|△U-f(x)dx|=o(dx)(dx→0)的基础上,对面积、体积、侧面积计算公式中的微元选取进行了详细的分析,并做了严格的证明.In the differential element method of definite integral,the selection of micro-elements is not arbitrary,but determined by certain requirements.If the requirements are not met,the calculation formulas obtained are wrong.On the basis of emphasizing that the selection of micro-elements must follow the following rule:|ΔU-f(x)dx|=o(dx),dx→0,the paper analyzes the selection of microelements in the calculation formulas of area,volume and lateral area in detail,and makes a strict proof.

关 键 词：定积分 微元法 微元 高阶无穷小 

分 类 号：O172.1[理学—数学]