On Pset #9, problem 4D #3, which is- 4D-3 Find the area inside the hypocycloid x2/3 + y2/3 = 1, by using Green’s theorem.
(This curve can be parametrized by x = cos3 θ, y = sin3 θ, between suitable limits on θ.)

Can ANYONE explain why they used the -ydx+xdy vector field to evaluate the hypocycloid? This entire problem confused me really.

Question

On Pset #9, problem 4D #3, which is- 4D-3 Find the area inside the hypocycloid x2/3 + y2/3 = 1, by using Green’s theorem.
(This curve can be parametrized by x = cos3 θ, y = sin3 θ, between suitable limits on θ.)

Can ANYONE explain why they used the -ydx+xdy vector field to evaluate the hypocycloid?  This entire problem confused me really.

phi · Answer

Perhaps this will help

anonymous · Answer

So they use it because in order for the double integral to actually equal the area inside the curve, Nx-My has to equal 1?  Okay.. that DOES make sense!  Thanks Phi!