Rosa ‘Flora Danica’

Since the divergence of a vectorfield provides us with the number of field lines radiating outward from the source of the vectorfield it can be intuitively understood that the volume integral of the divergenbde of F equals the surface integral of F over the closed surface A:

∫ ∇⋅F dv =  ∫F⋅dS 

Another important theorem in vaectoranalysis is Stokes Theorem
∫∇×F ds = ∫F⋅dl