Evaluate the surface integral:

integrate with respect to S (curl(f)).ds

where S is the open surface of the hemisphere x^2+y^2+z^2=a^2, z>0

with the outward normal chosen andfis the vector field:

f=(x+1)yi+y^2j+3x^2y^3zk

using

a)Stokes theorem

b)Gauss theorem