区域对称性和函数奇偶性在积分计算中的应用

Application of the Function's Parity and Domain's Symmetry to Calculate the Integrals

积分区域的对称性和被积函数的奇偶性不仅体现了数学美,而且可以使积分的计算变得简单又方便.通过对积分区域的对称性和被积函数的奇偶性的讨论,从积分区域关于坐标平面、坐标轴和坐标原点对称出发,建立了简化各类积分计算的常见公式,并用例子展示了公式的有效性.

The symmetry of integral domain and the parity of integrand not only reflect the beauty of math, but also make integral computation more simple and convenient. By use of symmetry of integral domain to coordinate surface, coordinate axis and coordinate origin, some useful formula to compute the integral are constructed,which are illustrated very useful and effective.