Help in proof (Green's Theorem)

[come2ershad]

Homework Statement

I have a doubt in proving the attached theorem. I have found that divergence theorem can be applied. However I am not able to arrive at the exact equation.

Homework Equations

Attached

The Attempt at a Solution

Derived the LHS. Couldn't proceed from there.

 

[come2ershad]

I consider u to be u1 i + u2 j and found the divergence. How to proceed from there?