Homework Help: Conceptual question on greens theorem/line integrals

1. Dec 4, 2012

Mdhiggenz

1. The problem statement, all variables and given/known data
Hey guys,

I just wanted to know, if it would be an incorrect assumption to say that greens theorem is directly correlated to a line integral.

The reason I am assuming that is because the formula for a line integral in my calc text is

∫f(x,y)dx+g(x,y)=∫f(x,y)dx+∫g(x,y)dy
c c c

Which is simply the left side of greens theorem.

I also am having a hard time putting the similarities between all three theorems. Greens, divergence, and stokes together in terms of what they all have in common.

Thanks

Higgenz

2. Relevant equations

3. The attempt at a solution

2. Dec 4, 2012

happysauce

Greens theorem is strict, the relation is true with a simple CLOSED contour but not in general. Take the line integral of a contour that isn't closed or simple and greens theorem will fail.

3. Dec 4, 2012

Mdhiggenz

How would we know if it fails?

4. Dec 5, 2012

happysauce

Small things like discontinuous functions would cause it to fail, if the contour isn't closed then it will most likely fail, if the contour is too complicated (it overlaps) then it will probably fail.