Stoke's and Gauss's Theorum in proving div(curlA)=0

[SquidgyGuff]

Homework Statement

The problem puts forth and identity for me to prove:

or

. It says that I can use "straight-forward" calculation to solve this using the definition of nabla or I can use Gauss's and Stoke's Theorum on an example in which I have a solid 3D shape nearly cut in two by a curve C.

Homework Equations

Divergence Theorum

Stoke's Theorum

The Attempt at a Solution

I just can't seem to figure out how to start this. The two equations above are clearly suited to proving this identity, but I just can't see how.

 

[ehild]

I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.

 

[SquidgyGuff]

I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.

Oh and I misstated the equality above, it specifies that the div(curlA)=0 then it has continuous second-order derivatives.