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The following question is right from the book:

Show that

$$ H(x-x_i) = \int_{-\infty}^x \delta(x_0-x_i)dx_0\, $$

satisfies $$ H(x-x_i) \equiv \begin{cases} 0 & x < x_i \\ 1 & x > x_i; \end{cases} $$

$\delta(\cdot)$ being the Dirac $\delta$ function and $H$ being the Heaviside unit step function.

Thing is, I don't know where to start on this question. How do you prove such a question?

Thanks in advance.

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What is your definition of $\delta$ and what properties do you know it to have? – Eckhard Jan 12 '13 at 12:18
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post. – Julian Kuelshammer Jan 12 '13 at 12:28
OP Since you accepted an answer 17 minutes after it was posted, this answer fully satisfies you. Maybe you could explain how it answers your question. Unrelated: which book is this exercise from? – Did Jan 12 '13 at 12:52
As far as I know the definition of the Delta function is correct. Though i do not quite understand the explenation with the integrals. The acceptance was a mistake. The Book is Haberman – InteressantPunt Jan 12 '13 at 15:25
Right. How exactly does Haberman define the Dirac "function"? – Did Jan 16 '13 at 20:30

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