Question

Please help me on how to evaluate this particular double integral. Let R be the region bounded by the graphs of the functions y=x,y=0,and x=4. Evaluate the double integral[4exp(x^2)-siny]dA

Answer 1

\[\int_0^4\int_0^x4e^{x^2}-\sin ydA\]hm... polar coordintes maybe?

Answer 2

\[\int_{0}^{\frac\pi4}\int_0^{4\sqrt2}[4e^{r^2\cos^2\theta}-\sin(r\sin\theta)]rdrd\theta\]not so sure what to do about that second term though...