Hi there, i am trying to do a proof that H'(t)= δ(t)
We have been given the following:
F is a smooth function such that lim (t-->±∞)F(t)=0
Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0
I understand it up until this point; however next it says:
"Integration by parts:
(1) = Integral between ±∞ of [H(f)'F(t)]dt
(2) = -the integral between ±∞ of H(t)F'(t)dt
(3) = -the integral between ∞ and 0 of F'(t)dt
(4) = [-F(t)]∞0
(5) = F(0)
(6) = Integral between ±∞ of δ(t)F(t)dt
The Attempt at a Solution
I dont know where they have got theequation from in (1) or (2) or (3)! I get 4 though and 5! Although i dont then get 6!
I think if i knew where (1) came from i maybe could get through the rest but i just dont know where it has come from?