The Question -

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

My Attempt-

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

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

$\displaystyle dA = rdrd\theta $

I got overall $\displaystyle \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 = $\displaystyle \int \int_{R} sin(\mid\sqrt{x^2 + y^2}\mid) $ in the same region