I have four problems i have no idea how to do: stokes theorem

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Use Stoke's theorem to evaluate where and S is the part of the paraboloid that lies inside the cylinder , oriented upward.

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Use Stoke's Theorem to evaluate where and is the boundary of the part of the paraboloid where which lies above the xy-plane and is oriented counterclockwise when viewed from above.

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Let . Use Stokes' theorem to evaluate the integral of around the curve consisting of the straight lines joining the points (1,0,1), (0,1,0) and (0,0,1). In particular, compute the unit normal vector and the curl of as well as the value of the integral:

,, (the unit normal vector)

,,

The value of the integral is ?.

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Let be the capped cylindrical surface which is the union of two surfaces, a cylinder given by , and a hemispherical cap defined by . For the vector field , compute in any way you like.