Can anyone please tell me significance of these corollaries of fundamental integral theorems? I can prove these corollaries but I don't understand why do we need to learn it? Do these corollaries have some physical significance? (a)$$\iiint_V(\nabla T)d^3 x=\oint_S T d\vec a$$ here S is the surface bounding the volume V . (b)$$\iiint_V(\nabla \times\vec v)d^3 x= -\oint_S\vec v\times d\vec a$$,where S is the surface bounding the volume V . (c)$$\iint_S(\nabla T)\times d\vec a =-\oint_P T d\vec l$$ , where P is the boundary of the surface S. .