Stokes's thm, Curl...

define the vector field F on the complement of the z-axis by F(x,y,z) = (-yi+xj)/(x^2+y^2) a). show that curl F=0 which i got my curl F =/= 0........ b). show by direct calculation ∫(c)Fdx=2πfor any horizontal circle C centered at a point on the z-axis. c). why do a). and b). not contradict... show more define the vector field F on the complement of the z-axis by F(x,y,z) = (-yi+xj)/(x^2+y^2)

a). show that curl F=0
which i got my curl F =/= 0........

b). show by direct calculation ∫(c)Fdx=2πfor any horizontal circle C centered at a point on the z-axis.

c). why do a). and b). not contradict Stokes's theorem?

Stokes's Thm:
∫(∂S)Fdx=∫∫(S)(CurlF)ndA
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