摘要:积分的计算是微积分学习中的一个难点.在积分的计算过程中，若能合理的利用对称性，则可以简化积分的计算过程.另外对称性在积分计算中的应用，还可以加深我们对积分概念的理解，提高我们学习积分的兴趣，培养我们善于发现生活中美的能力.本文介绍了对称性在积分计算过程中的一些结论及其应用，并且通过实例来讨论利用积分区域的对称性及被积函数的奇偶性简化重积分、曲线积分、曲面积分的计算的方法.在这个过程中要学会运用类比的思想，学会探究本质内容.

关键字：对称性；重积分；曲线积分；曲面积分；应用

Abstract:Integral calculation is a difficult point in calculus. In the process of integral calculation, one can simplify the integral calculation by use of the symmetry. On the other hand, the application of the symmetry in the integral calculation can also deepen the understanding of the concept of the integral, improve our interest in studying calculus and train the ability to find the fine things in our life. In this paper, we introduce some results and application on the symmetry in the integral calculation. Moreover, we will give some examples and discuss the methods to simplify the integral calculation by using the symmetry of the integral domain and the odevity of function. In these processes,we must learn to use the idea of analogy and to explore the essential contents.

Key words: symmetry; multiple integral; line integral; surface integral; application