# Green's theorem question?

#### Glitch

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

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

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

#### TheEmptySet

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

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

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

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

Glitch

#### Glitch

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