Okay, do know what "Stokes theorem" and "Gauss' theorem" are? If not, look them up! What do they say?
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 and f is the vector field:
f=(x+1)yi+y^2j+3x^2y^3zk
using
a)Stokes theorem
b)Gauss theorem
I imagine what HallsofIvy was implying was that these problems require a fairly straight forward application of the theorems. That is, you have the closed surface and a given vector; all that is left is to apply the definition of the theorems. So what have you done? Where are you stuck? If you show us some work we can show you where you went wrong! If you just want examples of how to typically solve these problems use google!