Closed Surface integrals and Gauss's Law

Question

I'm trying to understand Gauss's Law and I'm having some issue with understanding the notation.

I understand that $\oint_Cf(x)\cdot dx $ means taking the line integral on f(x) that ends at the beginning point. My question is what does $\oiint f(s)\cdot dA $ mean? Is it the sum of all possible closed line integrals across the surface or something else?

Also, does anyone know the Latex to get the \oiint to render on this?

Answer 1

What this is stating is that taking the line integral over the closed path is the same as taking the integral over the area that has the path as a extreme points $C = \partial A$. But they are not the same type of integrals, one is a line integral and the other is a integral over an area.

This is what I understand of your question. This notation means that you should calculate the integral over the closed surface related to the closed path $C$.

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MathJax doesn't support this symbol, so what you have is to use 'unicode'

$$\Huge\unicode{x222F}f(s)\cdot \mathrm dA$$