4. In this problem, we'll look at F(x, y) = T ()When a curve is a "closed loop" (that is, its starting point and ending point are the same), we often write f F . df rather than / F. di; the circle on the integral sign is just a reminder that C' is a closed loop. NC State Mathematics (a) You can check that (curl, F)(x, y) =0. Is it valid to conclude from Green's Theorem that for any simple closed loop C with interior R that F . dr = OdA = 0? Explain why or why not in a sentence or two. (b) Note that if f(x, y) = } In (x2 + y?) +7, then Vf(xy) = (Fly, Ity Now can you conclude from this whether F is conservative? Why or why not