Vector Calculus · Challenge problem

The folium of Descartes $x^3 + y^3 = 3xy$ has a loop in the first quadrant, traced by $x = \dfrac{3t}{1+t^3}$, $y = \dfrac{3t^2}{1+t^3}$ for $0\le t < \infty$. Use Green's theorem to find the area enclosed by the loop.