我们知道,对于对称区间[-a,a]上的定积分Ⅰ=integral form n=(-a) to a(f(x)dx),若f(x)为奇函数,则I=0;若f(x)为偶函数,则I=2 integral form n=0 to a(f(x)dx),这个结论对于某些定积分的计算是比较方便的。 关于坐标轴或坐标面对称区域上的重积分有与上面类似的性质,它对某些重积分的计算,也是方便的。这些性质是: 定理一 对于I=,若D关于y轴对称,记对称的两部分区域为 We know that I = 0 if f (x) is an odd function for a definite integral in the symmetric interval [-a, a] If f (x) is an even function, then I = 2 integral form n = 0 to a (f (x) dx). This conclusion is more convenient for the calculation of some definite integrals. The re-integration with respect to the axis of symmetry or the area of ​​symmetry of the coordinate plane has a similar behavior as above and is also convenient for the calculation of some double integrals. These properties are: Theorem One For I =, if D is symmetric about the y-axis, note that the symmetrical two-part region is