Integrals over different domains

[bugatti79]

Folks,

When we are evaluating integrals like the following, what are we evaluating in terms of units etc.

For example if I integrate Fdx I get an area which represents the energy where F is the force and d is the displacement so the units are Nm etc.

1) Integrals over intervals
?

2)Double integrals over 2-D regions

Is this an area of a 2d surface?


3)Triple integrals over 3-D solids

Is this an area of a 3d surface?


4)Line integrals along curves in 2-D space
5) Line integrals along curves in 3-D space

These 2 would not be an area becasue we are dealing with curves?


6) Integrals over surfaces in 3-D space?

Is this an area over 3-d surfaces/solids?

Hopefully some one can can clarify

I am asking this in the context of geometric surfaces like one would see in calculus books etc.

Thanks

 

[mathman]

In all cases it depends on what the integrand is.