- 9. Let's verify Stokes's theorem for the vector field v = (y, 2x2,2%), and the surface S parametrized by the paraboloi

[answerhappygod]

9 Let S Verify Stokes S Theorem For The Vector Field V Y 2x2 2 And The Surface S Parametrized By The Paraboloi 1 (45.85 KiB) Viewed 21 times

- 9. Let's verify Stokes's theorem for the vector field v = (y, 2x2,2%), and the surface S parametrized by the paraboloid z = R2 – x2 - y2 and constrained by a > 0. (a) First, determine the contour C that bounds this surface. [2 points) (b) Next, compute v. dx, fo i.e., the line integral along the bounding contour. You may find polar coordinates useful. [3 points] (c) Then, compute V xv. [3 points] (d) Now, parametrize the position vector for the surface Us = xs(t, u) (or use x,y). Then find the tangent vectors to this surface. Finally obtain the normal vector to the surface from the tangent vectors. [4 points) (e) Finally compute the surface integral [xvxo (V xv).ds and show that it is equal to your result from part(b). For parts (c) and (d), it made sense to use Cartesian coordinates, however, for the surface integral you may find polar coordinates to be convenient. [5 points)