对称性在积分计算中的应用

Application of Symmetry in Calculating Integral

积分学是《高等数学》中最基础,最重要的内容之一.在一元函数定积分中,奇偶函数在对称区间上的积分具有很好的性质,利用这些性质,将会大大简化某些积分的运算.事实上,对多元函数重积分、曲线积分和曲面积分而言,奇偶函数在相应对称积分域上也有类似结论.本文就针对这方面的问题进行了探讨并举例说明.

The integral calculus is one of the most primary and significant content in ＂Higher Mathematics＂. In the definite integral of one variable function, the parity function presents the good nature in symmetry intervals, which will greatly simplify the operation of certain integrals by using these properties. In fact, able integrals of many variables functions, curvilinear integrals and curved surface integrals as far as muhivari- are concerned, the odd-even functions present similar conclusions in the corresponding symmetry integral domain. This paper is aimed at these problems discussed and illustrated above.