Surface integrals

1. The problem statement, all variables and given/known data
Its more of a general issue of understanding than a specific problem

I have to evaluate a few surface integrals and im not sure about the geometric significance of what im evaluating or even of what to evaluate. Examples.

If n is the unit normal to the surface S evaluate Integral of: r . n dS over a) a unit cube. b) a sphere

Not sure what im evaluating or what the significance of it is. If someone could explain the general steps to take ill try and apply it to the specific problems

2. Relevant equations


3. The attempt at a solution

 

If i know what integral to do, i can do integration, its just a matter of knowing what I'm integrating. Is r a position vector? r.n gives us the projection of vector r onto the normal of the surface.

 

yeah ok it makes sense that all of the sides of a cube will have a normal that is just in the directions of one of the axis

Here is the question:
http://imgur.com/jqJTF5h

im struggling with pretty much all the questions there, but we are specifically talking about 4 here.

 

Im not entirely certain but ill give it a shot:

http://imgur.com/umVYFS3

 

ahh yeah i was wondering whether that would be right or not, itll be dydx then, which evaluates at 0 right? do i then sum all the sides?

 

oh, i see, so dydz / dzdy then? does order matter?
Thanks a bunch for your help and patience!
edit:typo