Use Green's Theorum to evaluate the line integral ∫c (x^2)y dx, where c is the unit circle centered at the origin.
The Attempt at a Solution
Taking the partial derivative with respect to y and subtracting it from zero(I'm taking the dy in the original problem to be zero because there wasn't one), I set up the double integral:
∫y = -1 to y =1 ∫x = -sqrt(1 - (y^2)) to x = sqrt(1 - ( y^2)) -(x^2) dxdy
I'm just kind of confused because there is no dy in the problem, and I'm not sure why the answer was -π/4.
I might not have set it up right because when I put the x bounds into -(x^3)/3, I'm not sure how to then integrate with respect to y.