Vector Calculus: Divergence theorem and Stokes' theorem

Hi =)

I've been working on some exercises, but unfortunately we are not given the answers, so have no idea if I am going wrong or not. I attemted part a) which reads:

**Consider the vector field**

__V__= 3x^2y__ i __ - 2xy^2 __j__ - xyz __k __

Determine the divergence of this vector field and evaluate the integral of this quantity over the interior of a cube of side a in z> or equal to 0, whose base has the vertices (0,0,0), (a,0,0), (0,a,0), (a,a,0).

Evaluate the flux of __V__ over the surface fo the cube and thereby verify the divergence theorem.

So for this I got both sides to be **1/4 a^5**

Its the next part that has got me completely confused! (its long, here goes..! if anyone can teach me how to use the integral symbols and stuff, i will edit this post to make more sense!)

[B]b) Given __V __= (3x-2y)__ i __ + x^2z __j __ + (1-2z) __k__

Find del.V and del x V and evaluate:[B]

I found them to be (3x-2y) __i__ + x^2y__ j __ + (1-2z)__k __

and -x^2__ i__ + (2xz-2) __k __ respectively.

[B]i) double integral of __V__.d__S__

over the circular region in the xy-plane bounded by x^2 + y^2 = a^2. Regard the area element as positive in the positive z direction.[B]

What is dS supposed to be?!

**ii) Evaluate**

the double integral of (del x __V__) . d__S__

over the same region.

iii) Evaluate

the closed loop integral of__ V__.d__r__

clockwise looking in the positive z direction around the circle x^2 + y^2 = a^2 in the xy-plane.

iv) Evaluate

the triple integral of (del x __V__)dV

over the volume of the hemisphere bounded by the spherical surface x^2 + y^2 + z^2= a^2 for z>0 and the xy-plane.

Which two answers provide a verification of Stokes' Theorem?

Thank you SO much