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