# Understanding Gauss's law

Here there are Maxwell equations https://en.wikipedia.org/wiki/Maxwell%27s_equations . Let's take the first in particular, Gauss's law. In its integral form, the left side is equal to the integral over the volume $\Omega$ of $\nabla \cdot E$ (because of Stokes's theorem). So I have a triple integral of $\nabla \cdot E$ on the left side, and a triple integral (over the same volume) of $\frac{\rho}{\epsilon_0}$ on the other side. I can't see what they mean by "differential equations". This equation in particoular becomes $\nabla \cdot E= \frac{\rho}{\epsilon_0}$. I just don't understand what this means. It seems like that if two integrals are equal, then their integrands are also equal, which is obviously false.