Answer
$$20.5648$$
Work Step by Step
$$\eqalign{
& \int_0^2 {\int_0^{4 - {x^2}} {{e^{xy}}} dy} dx \cr
& {\text{Using a computer algebra system to evaluate the }} \cr
& {\text{iterated integral, we obtain:}}{\text{}} \cr
& {\text{}} \cr
& \int_0^2 {\int_0^{4 - {x^2}} {{e^{xy}}} dy} dx \approx 20.5648 \cr} $$
