State Stokes' theorem.
Let be the surface in given by , where and is a positive constant. Sketch the surface for representative values of and find the surface element with respect to the Cartesian coordinates and .
Compute for the vector field
and verify Stokes' theorem for on the surface for every value of .
Now compute for the vector field
and find the line integral for the boundary of the surface . Is it possible to obtain this result using Stokes' theorem? Justify your answer.