一道二重积分问题

一道二重积分问题如图
2025-05-17 16:11:29
推荐回答(1个)
回答1:

f(y-x) = sin(y-x), x ≤ y ≤ 1+x
f(y-x) = 0, 其它
I = ∫<0, 1>sinxdx ∫sin(y-x)dy
= ∫<0, 1>sinxdx [-cos(y-x)]
= (1-cos1) ∫<0, 1>sinxdx = (1-cos1) [-cosx]<0, 1> = (1-cos1)^2