Evaluate double integral $\iint_A x^2\,dx\,dy$ Calculate double integral
$\iint_A x^2\,dx\,dy$
Where 
$$ A = \{(x,y)\in R^2 \| x^2 + y^2 \leq 1\}$$
I try do this with polar coordinates
$$0 \leq r \leq 1
$$$$
0 \leq \theta \leq 2\pi  
$$
But I failed (I'm getting zero, I'm not sure I've correctly written out the polar coordinates)
My integral
$$\int_0^{2\pi}\int_0^1(r\cos\theta)^2r\,dr\,d\theta$$

In polar coordinates we get the double integral
$$\int_0^1\int_0^{2\pi}r^2\cos^2\theta\cdot r\,d\theta\,dr=\int_0^1r^3\,dr\,\left.\frac12(\theta+\cos\theta\sin\theta)\right|_0^{2\pi}=\left.\pi\frac{r^4}4\right|_0^1=\frac\pi4$$
