# Math Help - Green's theorem question?

1. ## Green's theorem question?

The question
Suppose R is a closed region in the plane bounded by a closed non-self-intersecting, piecewise smooth plane curve $\tau$. Prove that the area of R is given by

$\frac{1}{2}\oint_{\tau}{x \ dy - y \ dx}$

I'm unsure of how to solve this. Could someone guide me? Thanks.

2. Originally Posted by Glitch
The question
Suppose R is a closed region in the plane bounded by a closed non-self-intersecting, piecewise smooth plane curve $\tau$. Prove that the area of R is given by

$\frac{1}{2}\oint_{\tau}{x \ dy - y \ dx}$

I'm unsure of how to solve this. Could someone guide me? Thanks.
Just apply Green's theorem

$\frac{1}{2}\oint_{\tau}{x \ dy - y \ dx} =\frac{1}{2} \iint_{D} 1+1 dA=\iint_D dA$

3. Thanks, I didn't realise it was that simple.