Let F be the vector field F(x,y,z) = (xe,-ye,2). The vector field G is given in terms of a function g: R^3 -> R by G(x,y,z) = (-y,x,g(x,y,z)).
a) Determine a function g such that curl(G) = F.
b) Sketch the surface S that is parametrized by (x,y,z) = (cos(t),3sin(t),(1-t)^2) where t ∈ [0,1] and θ ∈ [0,2π].
c) Evaluate ∫∫∫n·dS, where n is the upward pointing normal vector.