利用对称性计算积分域无方向性的积分

Utilizing Symmetry to Calculate Integral on Nondirectional Integral Domain

利用积分域的对称性简化积分计算是优先考虑的计算策略之一.如果积分域由对称的两部分组成且无方向性,若被积函数在对称点处的函数值相等,则积分简化成半个积分域上积分的2倍.若被积函数在对称点处的函数值相反,则积分为0.如果积分域具有轮换对称性,当对被积函数也做相应的坐标轮换时,积分值不变.

Using the symmetry of integral domain to simplify integral calculation is one of the priority calculation strategies. If the integral domain is composed of two symmetrical parts and the integral domain has no directionality , then the integral twice times reduced to half an integral domain if the value of integrand on the symmetrical points are equal; If the value of integrand on the symmetrical points are opposite, then the integral is zero. If the integral domain has translatable symmetry, then the integral value unchanged when the integrand also has been done with corresponding coordinate translation.