Q:let S be the surface x^2+y^2+z^2=1,z>=0.Use stokes theorem to evaluate
line integral of (2x-y)dx-ydy-zdz
where line integral is around circle x^2+y^2=1,z=0,oriented anti clockwise.
No F is not -- the condition is If F is conservative curl F = 0
If you calculate the line integral directly
z= 0 so F = (2x-y)i -yj
note this fails the test for conservative as well since d(2x-y)/dy does not equal d(-y)/dx
If you parameterize C by x =cos(t) y = sin(t)
you will also get pi