# Area of a 2D region (Green's Theorem)(?)

1. Nov 15, 2009

### xago

1. The problem statement, all variables and given/known data
Calculate the area of the region within x3 + y3 = 3xy. It can be parametrized by $$\gamma$$:[0,$$\infty$$] $$\rightarrow$$ R2 with $$\gamma$$=<3t$$/$$1+t3, 3t2$$/$$1+t3>.

2. Relevant equations

Area = 1/2 $$\int$$x*dy - y*dx

3. The attempt at a solution

My plan is to take the curve parametrized by $$\gamma$$=<3t$$/$$1+t3, 3t2$$/$$1+t3> and use the parametric equations as x = 3t$$/$$1+t3 and y = 3t2$$/$$1+t3. Then i simply just use the equation for area given by Green's Theorem Area = 1/2 $$\int$$x*dy - y*dx and compute the integral. Can anyone confirm if this is right or am I way off?

2. Nov 15, 2009

### LCKurtz

That should work like a charm.