(955, #11) Use Stokes' Theorem to evaluate
where F = < x2 z, x y2, z2
> and C is the intersection of the plane x + y + z = 1 and
the cylinder
x2 + y2 = 9. C is oriented
clockwise as viewed from above.
Solution: To start
Next, the parametric equations of the surface S are
| x = u cos(t) y = u sin(t) z = 1-u cos(t) - u sin(t) u = 0..3, t = 0..2 Pi |
Finally,
Consequently,
