Answer
Use polar coordinates and write $\iint_Rf(x,y)dA=\int_3^6\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} f(r\cos\theta,r\sin\theta)rd\theta dr$.
Work Step by Step
The region $R$ can be easily expressed as the set of points in polar coordinates, that is $R=\{(r,\theta)|3\leq r\leq 6,-\frac{\pi}{2}\leq \theta\leq \frac{\pi}{2}\}$.
We decide to use polar coordinates and write $\iint_Rf(x,y)dA=\int_3^6\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} f(r\cos\theta,r\sin\theta)rd\theta dr$.
