微元法求旋转体体积与侧面积的微元同一取法  

A Unified Method for Selecting Micro-elements in Calculations of the Volume and Lateral Area of a Rotating Body Using the Differential Element Method

作　　者：张杰华 韩明华 Zhang Jiehua;Han Minghua(School of science,Kaili University,GuizhouKaili 556011)

机构地区：[1]凯里学院理学院,贵州凯里556011

出　　处：《科技风》2024年第29期126-128,147,共4页

摘　　要：本文以微分“以直代曲”的几何意义为基础,利用切线段代替曲线段的思想,给出了微元法求旋转体体积与侧面积的微分元素同一取法,阐明了两者微分元素本质上均应是圆台所对应的微分元素。本文利用定积分的基本计算公式验证了取圆台微分元素的正确性,利用初等几何知识的结论说明了微元法求旋转体侧面积不能取圆柱面为微分元素的错误原因。This article is based on the geometric meaning of"replacing curves with straight lines"in differentiation,and uses the idea of tangent line segments instead of curved line segments to provide a unified method for determining the differential elements of the volume and lateral area of a rotating body using the differential element method.It is clarified that both differential elements should essentially be the corresponding differential elements of a circular truncated cone.This article uses the basic calculation formula of definite integral to verify the correctness of taking the differential element of a circular truncated con,and uses the conclusion of elementary geometric knowledge to explain the error reason why the differential element method cannot take the cylindrical surface as the differential element when calculating the lateral area of a rotating body.

关 键 词：旋转体 微元法 微分 

分 类 号：O13[理学—数学]