How to Evaluate Surface Integrals Using Divergence Theorem?

[Hoofbeat]

Please help! I'm soo confused with surface integrals and have several to do by tues for my tutorial. I don't really understand how to approach surface integrals! Could someone give me an over-view and help me through the question below - hopefully then I can manage the rest myself (Btw $ = integral sign)

Q. If n is the unit normal to the surface S, evaluate $$ r.n dS over:
a) the unit cube bounded by the coordinate planes and the the planes x=1, y=1 & z=1;
b) the surface of a sphere of radius a centred on the origin.

I *think* that I have to start by finding an equation for the cube (how?!) and then using divergence theorem but I really have no idea what I'm doing (I couldn't follow the lectures and books confuse me with their notation!

Thanks

 

[dextercioby]

I guess you needn't really know the "equations" for the surfaces of the cube and the sphere.Just some calculus,Gauss-Ostrogradski theorem & some basic space geometry...

How about posting your work...?

Daniel.

 

[Hoofbeat]

How about posting your work...?

That's the thing, I haven't done any of it! I'm genuinely confused as to even start the problem. I'm thinking I have to consider each face of the cube, but I really don't work well in 3D and can't even think how to express each plane as an equation! Then how do I progress? Do I have to calculate the Div or do it a different way I thought I was following the lectures ok as the first few were fine and I could do the respective problem sheets but with the last few lectures on surface integrals & Divergance I've been so confused!

 

[Galileo]

All you need is the Divergence (or Gauss's/Ostrogradksy's) theorem.
Try setting up the integral first. You don't have to parametrize the surface.