Integral multivariable equation on unit circle

Question

I have integral

$$\iint_D\frac{x}{\sqrt{x^2+y^2}} \,dx\,dy\,,$$

where $D$ is the unit circle's first quadrant

I've applied bounds to get

$$\int^1_0 \int^\sqrt{1-x^2}_0 f(x,y) \,dx\,dy$$

Answer 1

$$\int^1_0 \int^\sqrt{1-y^2}_0 \frac{x}{\sqrt{x^2+y^2}}\,dx\,dy=\int^1_0 \left.\sqrt{x^2+y^2}\right|_0^\sqrt{1-y^2}\,dy=\int^1_0 (1-y)\,dy$$

or in polar coordinates

$$\int_0^{\pi/2}\int_0^1\cos\theta\,r\,dr\,d\theta=\int_0^{\pi/2}\cos\theta\,d\theta\int_0^1\,r\,dr.$$