The curve defined by the relation x^3+y^3=3xy intersects itself at the origin and forms a loop. Find the area enclosed by the loop.

(In reply to re(2): A solution; Not quite by goFish)

"Integrating Sqrt[(3*x^2 - Sqrt[2]*x^3)/(3 + 3*Sqrt[2]*x)] between these values gives half the area (3/4)."

Can you please explain how you performed this integration?

Did you use a table of integrals, or did you use numerical integration, or did you use a series of substitutions, or what?

I used numerical integration and got the same result within a small tolerance.

Posted by Richard on 2005-12-16 14:09:55