左端交换积分次序得(积分域为三角形域,即0《x《a, x《y《a)左端=∫dx∫f(x)e^m(a-x)dy,(x的积分下限为0,上限为a;y的积分下限为x,上限为a)=∫f(x)e^m(a-x)dx∫dy,(x的积分下限为0,上限为a;y的积分下限为x,上限为a)=∫(a-x)f(x)e^m(a-x)dx,(x的积分下限为0,上限为a)=右端注:对y积分,x是常数,可将f(x)e^m(a-x)提到前一个积分号内;∫dy(y的积分下限为x,上限为a)=a-x