# Heaviside unit step- and delta function

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 being the Dirac delta function en H being the Heaviside unit step function.

Thing is, i dont know where to start on this question. How do you proove such a question?

What is your definition of $\delta$ and what properties do you know it to have? –  Eckhard Jan 12 '13 at 12:18