摘要
众所周知，在《数学分析》的定积分应用中，关于有向Ｊｏｒｄａｎ光滑曲线的弧长，给出了经过严格证明的三种形式的计算公式。但是曲线方程在极坐标情形下，当曲线的部分量用相应的小圆弧段长度近似代替时，所导出的公式，一般情况是不正确。这是一个在教学过程必然遇到的问题。本文就此问题给出了明确的回答和严格的证明。
In the application of the definite integration in mathematical analysis,there are three kinds of formula for the arc length of oriented Smoth Jordan curve which have been proved strictly.But when the curve equation is expressed with polar coordinates and the part of the quantity of the curve is approximatly replaced with the corresponding arc lingth, the deduced formula is incorrect. The above question is solved satisfactorily in the paper.
出处
《华北水利水电学院学报》
1995年第3期56-60,共5页
North China Institute of Water Conservancy and Hydroelectric Power
