evaluate double integral xz^2 dydz + (x^2y - z^3 ) dzdx +(2xy +y^2z ) dxdy where S is the hemisphere bounded by z = ( a^2 +x^2 + y^2) ^(0.5) and z= 0. solve by divergence theorem.

my working:

to use div theorem, the surface S has to be closed. so let S be the surface of a sphere and then divide the answer by half at the end.

the unit normal vector = <x,y,x > / a

having doing up to here, im stuck. what is the vector field based on the question? has my method been correct so far?