Vector Calculus: Stokes's Theorem?

Question

I'm a bit stuck on how to use Stokes's theorem to prove that one equation is equivalent to another. For example, how would i go about proving this?

Integral over a surface S of (R x (DEL times f)) . DS = minus the integral over the boundary of the surface S of ((f times R) . DR

Where R is a vector field, f is a scalar field, DEL is the differential operator, . is the dot product or divergence, and x is the cross product or curl.

I know i have to relate it to Stokes theorem, but i'm not sure how to do this. Any help would be greatly appreciated

Answer 1

Hmm, is R supposed to be curl-free (curl(R) = 0)? If so you can use the fact

curl(f R) = f curl(R) + (DEL f) x R

and apply Stokes Theorem to this.

Answer 2

this is incorrect.