2. Consider the conical surface S={(x,y,z)∈R3 : x2 + y2 = z2, 0 ≤ z ≤...

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2. Consider the conical surface S={(x,y,z)∈R3 : x2 + y2 = z2, 0 ≤ z ≤...

2. Consider the conical surface

S={(x,y,z)∈R³ : x² + y² = z², 0 ≤ z ≤ 1},

and the vector field

(a) Carefully sketch S, and identify its boundary ∂S.
(b) By parametrising S appropriately, directly compute the flux integral $\int \int$ _S (∇ × f) · dS.
(c) By computing whatever other integral is necessary (and please be careful about explaining any orien- tation/direction choices you make), verify Stokes’ theorem for this case.

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