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## Homework Statement

Hi there, i am trying to do a proof that H'(t)= δ(t)

## Homework Equations

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?