A little help is needed for the question below:
Find a simple, closed curve in $\mathbb{R}^2$ so the vector field $$F(x,y) = (2y + 4y^3 + 2xy^3, -5x^3 + 3x + 3x^2y^2 )$$ will have maximum circulation.
I guess it involves the Green's theorem and finding the line integral. But as the curve equation is unknown, I am not able to know the upper and lower boundaries for calculating the line integral. The double integral is $$\iint (-15x^2 - 12y^2 + 1) dxdy$$
Please give me some hints? Thank you!