I got this right out of a fluke, but cannot understand the solution given:
The explanation given sounds like both of them are right. The variables inside the parentheses are just shuffled around which should make no difference. Honestly, one is more inclined to believe the first one is right due to similar arrangement of variables. Can someone tell me what I am missing here?
The first triple integral gives $f_U(a)$ and not $f_Y(a)$ so the equation is wrong. The second one is right.