Let $f(x,y) = x^2\sqrt{x^2 +y^2}$ and domain $D = \{(x,y) : x^2 +y^2 \le 4 \ , 0\le y\le x\}$. Find value of
$$\iint_D f(x,y) \ dx dy$$
I tried to use $x = r\cos \theta$ , $y = r\sin \theta$ and then got: $$\iint_Df(x,y)\,dxdy=\int_0^{\pi/4} \int_0^{2} (r^3\cos^2\theta)\cdot r\,drd\theta =\frac{\pi +2 }{8}\cdot\frac{32}{5}$$
I don't know whether this answer is correct or not.