Divergence theorem in maths

In vector calculus, the divergence theorem, as well known as Gauss' theorem, Ostrogradsky's theorem, or Gauss-Ostrogradsky theorem is an answer that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface.

More accurately, the divergence theorem states that the outward flux of a vector field through a surface is equal to the triple integral of the divergence on the region in the surface. Intuitively, it states that the sum of every source minus the sum of all sinks gives the net flow out of a region.
The divergence theorem is the main result for the mathematics of physics, particularly in electrostatics and fluid dynamics.