∫[0,1] dx ∫[0,1-x] 1/2*e^(-y/2) dy
=∫[0,1] dx ∫[0,1-x] -1 * e^(-y/2) d(-y/2)
= -1 *∫[0,1] dx { e^(-y/2)|[0,1-x]}
= -1 *∫[0,1] { e^[(x-1)/2] -1] } dx
= -2 *∫[0,1] { e^[(x-1)/2] -1} d[(x-1)/2]
= -2 *{ e^[(x-1)/2] -(x-1)/2 } | [0,1]
= -2 *{ 1 - [e^(-1/2) +1/2] }
= 2e^(-1/2) - 1
答案会和正确答案正负号是相反的,
可能是凑微分的时候少算了负号,也可能是代人积分限时算反了,没有具体的例子也不好说确切是什么地方出错啊.