Use Green's Theorem to evaluate the integral of y^4 dx + 2xy^3 dy, where C is the positively defined ellipse x^2+2y^2=2.

I know the inside of the integral ends up being -2y^3 dA but I can not figure out the limits of integration. I converted the C to the standard form for an ellipse and got x^2/2 +y^2 =1. Parameterizing this gives x=sqrt(2)cost and y=sint

Question

Use Green's Theorem to evaluate the integral of y^4 dx + 2xy^3 dy, where C is the positively defined ellipse x^2+2y^2=2.  

I know the inside of the integral ends up being -2y^3 dA but I can not figure out the limits of integration.  I converted the C to the standard form for an ellipse and got x^2/2 +y^2 =1.  Parameterizing this gives x=sqrt(2)cost and y=sint

abb0t · Answer

did you make sure that it meets greens theoirem?