Find the area of the region enclosed by the parametric equation x = t^3−3t y = 6t^2.

Answer 1

The loop is formed when x=0, or t=±√3

So, the area is

∫[-√3,√3] y(t) dx/dt dt
= ∫[-√3,√3] (6t^2)(3t^2-3) dt = 144√3/5