The theorem was first discovered by Lagrange in 1762, then later independently rediscovered by Gauss in 1813, by Ostrogradsky, who also gave the first proof of the general theorem, in 1826, by Green in 1828, etc. Subsequently, variations on the divergence theorem are correctly called Ostrogradsky's theorem, but also commonly Gauss's theorem, or ...

*Divergence Theorem Let \(E\) be a simple solid region and \(S\) is the boundary surface of \(E\) with positive orientation. Let \(\vec F\) be a vector field whose components have continuous first order partial derivatives.*Gauss Divergence theorem states that for a C 1 vector field F, the following equation holds: Note that for the theorem to hold, the orientation of the surface must be pointing outwards from the region B, otherwise we’ll get the minus sign in the above equation. Volumes calculation using Gauss' theorem As with what it is done with Green's theorem, we will use a powerful tool of integral calculus to calculate volumes, called the theorem of divergence or the theorem of Gauss. Volumes calculation using Gauss' theorem As with what it is done with Green's theorem, we will use a powerful tool of integral calculus to calculate volumes, called the theorem of divergence or the theorem of Gauss.