重积分的对称性质

Symmetric Properties on n-fold Integrals

在重积分的计算中,经常要用到对称性质.而限于时间和篇幅,现行大多数教科书上都不加讨论的引用对称性质.这就使初学者感到重积分的对称性质不好掌握.本文通过重积分的变量替换公式,给出重积分对称性质的一个一般定理和两个推论,最后给出一个具体实例.

The symmetric properties often are used in calculating n-fold integrals. Many teaching materials cite directly these properties without any discussion because limited by teaching time and volume of teaching material. As a result,many students feel diffcult understand these properties in study. In this note,a theorem and two corollaries are obtained by means of the formula of transformation of n-fold integrals variable. A example is given to illustrate the application of the theorem in this note.