[7.4.5] Let C be any smooth simple closed curve with positive orientation that lies entirely in a plane with unit normal vector field in = (-2/3, 2/3, 1/3), and let F = (3y, 9:, 62). Find the circulation around C as a function of the area A inside C. Follow these steps: (1) There is no parametrization to consider, as C is arbitrary. (2) Compute V x F(x, y, z). 13) Compute V x F(x, y, z) . n. (4) Set up and evaluate the surface integral ( v x F . as = V X F. idS. The integration itself is one step, if you recognize what's going on. Your final answer will contain A. Remark: here is the reason why parts (3)-(4) work. Suppose we did have a parametrization T(u, v), oriented correctly. Then ds = Tu X T, du du = Tu XTU IT UX Toll Tu X Tull dudu = nds, ds