2. Let S be the portion of the parabaloid 2 = 1 :52 y2 that lies above the cryplane, with a normal direction oriented away from the origin, and let F = zi + :Ej + yk. We wish to use Stokes' theorem to compute the value of / curlF - (1A. 5 (a) Are the requirements for Stokesj theorem satised? Yes, 3 is a smooth oriented surface and the boundary of S is a. piecewise smooth curve (It is the unit circle in the ritzy-plane). Furthermore, F is a smooth vector eld, meaning that all if its components have partial derivatives that exist. (b) If we apply Stokes' theorem, what does it say for this particular problem. On one hand, we could evaluate the integral as stated. On the other hand, we could apply Stokes1 theorem and evaluate a different integral and we would be guaranteed to get the correct answer. We would need to evaluate fF-d'r 0 Where C is the bom'idary of 3, 1e. it is the unit circle: :1: = cos(t), y = sin(t), z = 0 oriented counter clockwise as viewed from above. (c) Compute / F-a'r. c f F rrrr / F( (r). are. (m m romarzorndt / Mr): mart- dr l)