$D=\{(x,y)\mid x^2+y^2 \le x\}$ , by changing to polar coordinate, find this integral: $$\iint_{D}\sqrt x\,dx\,dy$$
So I got this by changing to polar coordinate
$$\int_{-\pi/2}^{\pi/2}\int_{0}^{1/2}\sqrt{r\cos \theta}\ rdr\,d\theta$$
First is my limit for integral true?
And I don't know how to integrate $\sqrt {r\cos\theta} $ here.
Thank you!