Let V be a region in space with boundary dV. Then the divergence theorem states that the volume integral of the divergence divergence F of F over V and the surface integral of F over the boundary dV of V are related by integral_V divergence F dV = integral_(dV)F·da.

Gauss-Ostrogradsky theorem | Gauss's theorem | Ostrogradsky's theorem

formulation date | 1762 (263 years ago) formulator | Joseph-Louis Lagrange status | proved proof date | 1826 (64 years later) (199 years ago) prover | Mikhail Vasilevich Ostrogradski additional people involved | Carl Friedrich Gauss | George Green

integral_V divergence F dV = integral_(dV)F·da

solved mathematics problems | mathematics theorems