对称弧段上的对弧长的曲线积分的研究

Discussion on Curvilinear Integrals with Respect to Arc Length on Symmetrical Segment of a Curve

主要讨论平面上对弧长的曲线积分的计算。首先利用曲线c关于坐标轴奇偶函数的定义,给出了曲线c关于任意直线的奇偶函数的定义,将奇偶函数在对称于坐标轴的曲线弧段上的对弧长的曲线积分计算公式推广到了在对称于平面上任意一条直线的曲线弧段上的对弧长的曲线积分计算公式,并且给出了证明。其次利用此公式,讨论了某些函数在封闭曲线弧段上对弧长的曲线积分的计算问题。可以看出,这一公式的使用,简化了繁杂的计算过程,有明显的实用价值。

This article discussed the calculation of the curvilinear integrals with respect to arc length in a plane.Firstly,from the definition of curvilinear C about parity function to coordinate axis,the definition of curvilinear C about parity function to any straight line was deduced.Also,the integral formula of parity function on arc length of curve symmetric to coordinate axis was extended to arc length of curve of any straight line in a plane.Meanwhile,the demonstration of that extension was presented.Secondly,on the basis of this function,the calculation problem of the curvilinear integrals with respect to arc length of a function on a closed curve arc was discussed.It is obvious that this formula greatly simplified the calculation process and had excellent practical value.