# Homework Help: Simple integration question involving-infty subscript

1. Sep 17, 2011

### Salt

simple integration question involving-infty "subscript"

1. The problem statement, all variables and given/known data

Been reading about signals, but my calculus skills have rusted (or never has been all that good in the first place).

So ...

2. Relevant equations

Why does $x(t) = \int^t_{-\infty} x'(\tau) \,d\tau$ ?

3. The attempt at a solution

You will end up with $x(\tau)|^t_{-\infty} = x(t) - x({-\infty})$. Right?

So $x({-\infty}) = 0$ for all functions?

Been looking on the web, but I have no idea how to google this.

2. Sep 17, 2011

### Staff: Mentor

Re: simple integration question involving-infty "subscript"

No, you can't do this. Infinity is not a number that you can substitute into a function. Your integral is one type of improper integral. To evaluate an integral like this, you need to work with a limit, like so:
$x(t) = \int^t_{-\infty} x'(\tau) \,d\tau = \lim_{a \to -\infty} \int_a^t x'(\tau) \,d\tau$

3. Sep 18, 2011

### Salt

Re: simple integration question involving-infty "subscript"

Hmm ...

Looks like my calculus really does suck.

It was just written "like that" in the book. It probably assumes that I know how to solve it. ><

Thanks.

Last edited: Sep 18, 2011