Line/Surface integral question (no computation required)

Quote:

Originally Posted by godiva

I just can't get my head around these line integrals and their difference.

When do I use:

$\int_C F \cdot dr = f(B) - f(A)$

Green's theorem which is $\oint_C F\cdot T ds = \int \int (curlF) \cdot k dxdy$

Divergence theorem: $\int \int_S F \cdot n d\sigma = \int \int \int divF dV$

and Stokes theorem which is $\oint F \cdot dr = \int \int CurlF \cdot n d\sigma$

Can someone explain clearly when to use each one because to me, all the questions kind of look the same. Anyone know any tricks?

The first formula is just standard formula for integration along a non-closed path- a path that has two distinct endpoints.

Green's theorem and Stoke's theorem are almost the same- Green's theorem applies to a closed path in the xy-plane, Stoke's theorem to a closed path in three dimensions.

The divergence theorem has nothing to do with "paths". It relates the integral on a closed surface to the integral over the region inside that surface.