Compute the line integral of the vector field F=<3y,-3x> over the circle x^2+y^2=4 oriented clockwise

∫c F · dr
= -∫c' (3y dx - 3x dy), where C' has counterclockwise orientation
= -∫∫ [(∂/∂x) (-3x) - (∂/∂y) (3y)] dA, by Green's Theorem
= ∫∫ 6 dA, where we are integrating over the interior of x^2 + y^2 = 4
= 6 * (Area of the circle with radius 2)
= 24π.

I hope this helps!