Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector field, surface S, and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation. F= (y. - x, 15) ; S is the upper half of the sphere x? + + z? = 16 and C is the circle x?+ y?= 16 in the xy-plane. Construct the line integral of Stokes' Theorem using the parameterization r(!) = (4 cost,4 sin t, 0), for Osts 2it for the curve C. Choose the correct answer below. 2x O A. - 32 dt 2x O B. 16 dt 0 2x O c. 32 dt 2m OD. - 16 dt Construct the surface integral of Stokes' Theorem using R = {(x,y): x"+ y's 16) as the region of integration. Choose the correct answer below. OA. - 2JJ dA R OB. 4/JdA R Oc. 2 dA R OD. - 4 / JdA R Evaluate both integrals to verify that they are equal. What is the result? (Type an exact answer, using it as needed.)