Question

Use Stokes' Theorem to evaluate
C
F · dr
where C is oriented counterclockwise as viewed from above.
F(x, y, z) = yzi + 9xzj + exyk,

C is the circle
x2 + y2 = 1, z = 3.

Answer 1

curl of F over the surface
curl is
i j k
d/dx d/dy d/dz
fx fy fz

is
=(dFz/dy-dFy/dz)i
+(dFx/dz-dFz/dx)j
+(dFy/dx-dFx/dy)k

here Curl F
=(ex-9x)i
+(y-ey)j
+(9z-z)k