(1 point) Calculate the circulation, [C 13- [IE in two ways, directly and using Stokes' Theorem. The vector field I? = 83;? 8x; and C is the boundary of S, the part of the surface 2 = 16 x2 y2 above the xy-plane, oriented upward. Note that C is a circle in the xyplane. Find a r70) that parameterizes this curve. ?(t) = , with S f S (Note that answers must be provided for all three of these answer blanks to be able to determine correctness of the parameterfzatr'on.) With this parameterization, the circulation integral is [C I? - d? = f: dt, where a and b are the endpoints you gave above. Evaluate your integral to find the circulation: [C 1*: ~ d? = Using Stokes' Theorem, we equate [C I? - d7 = [S curl I? ~ d1; Find curl I? = Noting that the surface is given by z = 16 x2 yz, find a? = dy dx. With R giving the region in the xyplane enclosed by the surface, this gives [5 mi aunt: [R dydx. Evaluate this integral to find the circulation: [CF-air = [ScurlF-dA =