Integral Signs

In calculus, we meet this fellow:

∫

And in multivariable calculus, we meet these folks:

∬ ∭

If we go on to complex analysis, we meet this guy:

∮

But what's a legitimate usage of these guys?  

∯ ∰

Are they deprecated symbols which are avoided in favor of the above, with slightly different notation?  Are they only used in complex analysis?

>>1
Closed area and volume integrals, what about them?

I'm just curious what an appropriate instance of use for the last two symbols is/are; I never encountered them in school, but always wondered where they are used.  Even wikipedia's own pages on the so-called "surface integral" and "volume integral" use ∬ and ∭ instead.  But the presence of the circle device suggests that the last two characters have something to do with the complex numbers...  I suck at math so I'm asking someone to spell it out for me.

∫ line integral - ∮closed line integral, a loop, etc.
∬Surface integral - ∯ Closed surface integral, like when you say the magnetic flux over a closed surface is 0, you use that.
and so on. Those are just physic interpretations.

>>4
And they're not directly related to complex analysis, just that the line integral happens to be used in complex analysis theorems as well as the closed line integral.

>If we go on to complex analysis, we meet this guy:

>∮

Never saw green's theorem on multivariable calculus?

>>6

as I learned it at the time, Green's theorem was not stated using that symbol, no.

>>7
But at least you now understand the use of closed integrals, right?

>>8

after a little more poking around, what I'm guessing is that the "circle" integral symbols can be used to refer to integrating over simple, closed one, two, and three dimensional manifolds, respectively, whether such manifolds are in R^2, R^3 etc, or in the complex plane, whereas the other signs denote the most "generic" forms of their respective integration.

i met ∮ in physics 2 when learning Gauss' law.

Just use the normal integral. You can see the bounds and dimension from context.