Solve double integral

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$$ \int_0^2 \int_0^{4-x^2} \frac{xe^{2y}}{4-y} \, dy\, dx $$

I'm stuck with this problem. I think I should change it so I integrate with respect to $dx \, dy$ but I'm not sure. Any help? Thanks

2

There are 2 best solutions below

4
On

Yes, integrate first with respect to $x$, where $x$ goes from $0$ to $\sqrt{4-y}$. That will cancel the nasty $4-y$ at the bottom.

10
On

Hints:

$$\int_0^4\int_0^{\sqrt{4-y}}\frac{xe^{2y}}{4-y}\,dx \,dy$$

Does it ring a bell?