Double integral $\displaystyle \int \int_{D} (x^3 + xy^2) dx dy $ where D is the ring domain $\displaystyle 1 \leq x^2 +y^2 \leq 2$

My solution:

$\displaystyle x=r cos\theta $

$\displaystyle y=r sin \theta$

$\displaystyle \int_{0}^{2 \pi} \int_{1}^{2} (r^3 cos^3 \theta +r cos \theta r^2 sin^2 \theta) r dr d\theta =0

$