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.