浅谈对称性在曲线积分计算中的应用

Discussion on the application of symmetry in curve integral calculation

积分在微积分学中既是重点又是难点,尤其是在解决积分的计算问题上,方法比较灵活、多样。本文着重讲述了常见的有关对称性在曲线积分、曲面积分计算中的几个重要结论,并结合实例进一步验证了:在积分运算中,利用曲线、曲面的对称性和函数的奇偶性,简化曲线或者曲面积分过程,使积分计算更加方便、迅速.进而说明对称性在计算曲线积分、曲面积分中的可行性与优越性。

Integral in the calculus is both emphasis and difficulty,especially to deal with the problem of integral calculation,the method is more flexible and diverse.This paper tells the common about symmetry in curvilinear integral calculation of several important conclusions,combined with the instance:further verified using the symmetry of integral area of and the parity of integrand to simplify the calculation of curvilinear integral,and then explain symmetry in computational feasibility and superiority of curvilinear integral.