Using the Shifting property of unit impulse, prove that Solution given the function (at) by shifting property f(t)(td)dt=f(d) so by using the shifting property let f(t) = (at) integral ( - infinty to + infinty ) (at) (td)dt let at = P a dt = dP integral ( - infinty to + infinty ) (P) (td)dP / |a| = (P) /|a| = (t) / |a| hence proved.