What does the new integral in surface integral theory represent?

[andyb177]

Watching video http://www.khanacademy.org/video/introduction-to-the-surface-integral?playlist=Calculus
at 20.10 the guy introduces the concept of what it means for each part of the surface to have a value of a new function f(x,y,z). Could some one explain what this new integral would represent?

My Three ideas are..
A volume between the two surfaces,
Just the surface area of the new surface f(x,y,z) which takes value from the param. surface in order to 'create it self'?
If the second one (which I think is more likely) why not create a param. to map straight to this surface?
Or is it something in 4d?

Thanks a lot.

 

[LCKurtz]

Watching video http://www.khanacademy.org/video/introduction-to-the-surface-integral?playlist=Calculus
at 20.10 the guy introduces the concept of what it means for each part of the surface to have a value of a new function f(x,y,z). Could some one explain what this new integral would represent?

My Three ideas are..
A volume between the two surfaces,
Just the surface area of the new surface f(x,y,z) which takes value from the param. surface in order to 'create it self'?
If the second one (which I think is more likely) why not create a param. to map straight to this surface?
Or is it something in 4d?

Thanks a lot.

I didn't want to bother watching the video. But an example of what I think you are describing would be a surface with a variable area mass density δ(x,y,z) given in units like, for example, kg/m². Then

$$\iint_S \delta(x,y,z)\, dS$$

would represent the mass of the surface in kg.

 

[andyb177]

Bang on, cheers