Why are Maxwell's equations sometimes written with one integral and other times they are written with two? For example, Gauss's law is sometimes written as 
$$∮E.da,$$
 but other times it is written as 
$$∯E.da. $$
How is taking a single integral the same as taking a double integral?
 A: It's just a difference in notation, where the double integral form is being explicit that the integral is over a two-dimensional domain. In the single integral form it is understood that the domain is two dimensional, and it is up to the person doing the calculation to figure out how to do the partition. Normally, there's even a symmetry involved that makes one of the integrals trivial, so we say things like:
\begin{align}
\oint \mathbf{E}\cdot \operatorname{d}\mathbf{A} & = \frac{1}{\epsilon_0} \int \rho \operatorname{d}V \Rightarrow \\
\mathbf{E}\cdot \hat{r}\, 4\pi r^2 & = \frac{1}{\epsilon_0} \int_0^r \rho(r')\, 4\pi r'^2 \operatorname{d}r',
\end{align}
for a spherically symmetric charge density, $\rho(r)$. This is even though the left hand side is a two-dimensional integral ($\oiint$, for some reason StackExchange isn't parsing the closed double integral symbol), and the right hand side is a triple integral ($\iiint$). More specifically, the left hand integral is over the boundary ($\partial V$) of the volume on the right hand integral ($V$).
I think the origin of this practice could be related to the study of measure theory, where you'll notice that there is only a single sum related to the integral, and the details of how the domain is partitioned are left open (see also: Hausdorff measure and metric space).
