# Green's theorem question?

• Jun 3rd 2011, 08:07 PM
Glitch
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.
• Jun 3rd 2011, 08:12 PM
TheEmptySet
Quote:

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

$\frac{1}{2}\oint_{\tau}{x \ dy - y \ dx} =\frac{1}{2} \iint_{D} 1+1 dA=\iint_D dA$
• Jun 3rd 2011, 08:24 PM
Glitch
Thanks, I didn't realise it was that simple. :)