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

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.