Consider the conical surface

S={$\displaystyle {(x,y,z) \in R^3 |x^2+y^2=z^2,0 \leq z \leq 1}$}

and the vector field f(x,y,z) = (-y,x,z)

(a) Carefully sketch S (can anyone please send me a picture?)

(b) Evaluate the path integral $\displaystyle \oint f.dr $ by direct integration.

(c) Confirm that $\displaystyle \int \int_{S} \nabla x f.dS $ gives the same value, as asserted by Stokes' theorem.

Thanks in advance