we are to show a=(1/2) closed loop integral over [r x dl]

I suppose this can be done formally from the alternative form of Stokes' theorem that can be obtained by replacing the vector field in curl theorem by VxC where C is a constant vector

The identity is :

surface int [(da x grad) x V]=closed loop integral over [dl x V]

The RHS matches.But how to show that LHS leads to the required value?