I've come across a Green's Theorem proof that has me perplexed.
Using the area formula: $$A = \frac{1}{2}\int_C xdy - ydx $$ Prove that:$$A = \frac{1}{2}\int_a^b r^2d\theta$$for a region in polar coordinates.
I assume a parametrisation is needed, but I'm not sure where to start due to the change in variables. My first thoughts are to change coordinates to $x=rcos\theta$ and $y=rsin\theta$. I also have assumed the $r^2$ is a result of the Jacobian being $r$ and some simplification of the $cos^2\theta + sin^2\theta$ identity.
Any help would be appreciated.
Thanks!