关于n重积分对称性的一点思考

Thoughts about the Symmetry of N-fold Integrals

本文从多维度的视角通过定义n维空间两个点的对称以及两个集合(区域)的对称,把奇偶函数在对称区间求定积分的性质推广到了n维空间求n重积分,对定积分、重积分对称性计算公式在形式上进行了统一.利于n重积分的简便、快捷、正确计算.

From several perspectives,this paper defines the symmetry of two points and the symmetry of two sets in the n-dimensional space,generalizes the properties of integration of even or odd functions on a symmetry interval to the n-fold integration,and unifies the calculation formulas for the symmetry of the definite integral and n-fold integral.A simple and fast calculation of n-fold integrals is followed.