# Thread: Surface Integrals, Stokes Theorem, Divergence Theorem, all the same?

1. ## Surface Integrals, Stokes Theorem, Divergence Theorem, all the same?

So am finishing up calc 3 and we are doing surface integrals, stokes' theorem, and divergence theorem.

But solving all the problems gets really confusing because I feel like all the different methods get mixed up. For example, in my book for the section on Stokes' theorem they might say evaluate using Stokes' Theorem but they will use the line integral method.

How do I know when I can use the method involving Curl F dS or F dr.
I know I am probably not providing enough info, but I hope you guys know what I mean.

2. Originally Posted by wizrd54
So am finishing up calc 3 and we are doing surface integrals, stokes' theorem, and divergence theorem.

But solving all the problems gets really confusing because I feel like all the different methods get mixed up. For example, in my book for the section on Stokes' theorem they might say evaluate using Stokes' Theorem but they will use the line integral method.

How do I know when I can use the method involving Curl F dS or F dr.
I know I am probably not providing enough info, but I hope you guys know what I mean.
It just depends, using Stokes Theorem makes the problem easier than taking the line integral. Normally the integration is alot easier and you don't have to worry about setting up you line integral correctly. Same thing with the divergence theorem. It is alot easier to use the divergence theorem than take the surface integral of each side.

3. I guess that makes a bit more sense.

Are there Surface Integrals where you can't use Stokes' or the Divergence Theorem?

I think it would help my understanding if you could tell me in what cases one method is better than the other. So the Divergence Theorem is good for finding surface integral of an object with many sides?

4. Originally Posted by wizrd54
I guess that makes a bit more sense.

Are there Surface Integrals where you can't use Stokes' or the Divergence Theorem?

I think it would help my understanding if you could tell me in what cases one method is better than the other. So the Divergence Theorem is good for finding surface integral of an object with many sides?
The Divergence theorem only works for a completely closed surface, for example a sphere, cube, or any closed surface.

So lets say you had to take the surface integral of a cube. It would be a pain because you would have do all 6 sides. Using the divergence thoerem it would be much easier because all you would do is take the divergence and then do a triple integral. Alot less work.