三重积分的对称性及其应用

The Symmetry and Application of Trible Integral

将一元奇偶函数及其在对称区间上的积分公式进行推广,得到了三元奇偶函数在对称区域上的定义及其积分公式,并给出了积分区域关于积分变量轮换对称时三重积分的计算方法,以简化某些积分的计算。

In this paper efforts have been made to extend the integral formulae of one-variable odd-even function in symmetric interval. Thus we’ve got the definition and integral formulae of three-variable odd-even function in symmetric area. In addition,we’ve also discussed the triple integral calculation when the integral area is the alternation of integral variable and simplified the calculation of some integral.