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

[xago]

Homework Statement

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>.

Homework Equations

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

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?

 

[LCKurtz]

That should work like a charm.