Suppose we have some well behaved curve y=f(x) lying in a plane. The length of a curve is given by

L = int( sqrt( 1+f'(x) ) )dx

I want to express this integral using the delta fuction as an integral over some area

A = int( delta( y-f(x) ) )dxdy.

Can this be done? If so, how to prove it?

Thanks.