The problem doesn't seem like it should be too difficult, I have a box-like region $B$ defined as: $$ \begin{align} 0 \le x \le 1\\ 0 \le y \le 3\\ 0 \le z \le 2 \end{align} $$ And the function to integrate is: $$ \int \int \int_B ye^{-xy}dV $$
So I set about it and did the following: $$ \begin{align} &= \int_0^2 \int_0^3 \int_0^1 ye^{-xy}\:dx\:dy\:dz\\ &= - \int_0^2 \int_0^3 \left[e^{-y} \right]_0^1 \:dy\:dz\\ &= - \int_0^2 \int_0^3 e^{-y} - 1\: dy\:dz \\ &= \int_0^2 \left[ e^{-y}-y \right]_0^3\:dz \\ &= \int_0^2 e^{-3} - 3\: dz\\ &= 2\:( e^{-3}-3) \end{align} $$ However my homework application states that this is not the correct answer. I am not sure what I did not do correctly. Can someone point me in the correct direction?
The problem was with my integration as @lulu pointed out. The correct answer after my integration goof-ups were fixed is $2 (e^{-3} + 2)$, which agrees with wolframalpha.