## Area of a plane circle (Polar co-ordinates)

The Question -

Calculate V = $\int \int_{R} sin(\sqrt{x^2 + y^2})$ where R is the region inside the circle $x^2 + y^2 = 4\pi^2$

My Attempt-

Since $r^2 = x^2 + y^2 ..... r = 2\pi$

the limits of integration i got were $0 \leq \theta \leq 2\pi$ and $0\leq r \leq 2\pi$

$dA = rdrd\theta$

I got overall $\int^{2\pi}_{0} \int^{2\pi}_{0} rsin(r) dr . d\theta$

Can someone please let me know if i'm on the right track and also what changes I would have to make to find W = $\int \int_{R} sin(\mid\sqrt{x^2 + y^2}\mid)$ in the same region