(955, #9) Use StokesÆ Theorem to evaluate

(955, #9) Use Stokes' Theorem to evaluate

where F = < 2 z, 4 x, 5 y> and C is the curve of intersection of the plane z = x +4 and the cylinder
x² + y² = 4. C is oriented clockwise as viewed from above.

Solution: First

Second, the parametric equations of S are

x = u cos(t)

y = u sin(t)

z = 4 + u cos(t)

u = 0..2, y = t = 0..2 Pi

Finally

Thus