Symmetric Properties on n-fold Integrals

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.