I have $\displaystyle \int\int_Rx^3+xy^2dxdy$,

$\displaystyle R$ = second quadrant of $\displaystyle 1/4<=x^2+y^2<=1$

I changed $\displaystyle x^3+xy^2$ to polar coordinates:

$\displaystyle r^3cos^3(\theta)+r cos(\theta)r^2sin^2(\theta)=r^3cos(\theta)$

Do I evaluate the integral like this?

$\displaystyle \int_{\pi/2}^{\pi}\int_{1/2}^{1}r^3cos(\theta)drd\theta$