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Homework Help: Simple integration question involving-infty subscript

  1. Sep 17, 2011 #1
    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 [itex]x(t) = \int^t_{-\infty} x'(\tau) \,d\tau[/itex] ?

    3. The attempt at a solution

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

    So [itex]x({-\infty}) = 0[/itex] for all functions?

    Been looking on the web, but I have no idea how to google this.
  2. jcsd
  3. Sep 17, 2011 #2


    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:
    [itex]x(t) = \int^t_{-\infty} x'(\tau) \,d\tau = \lim_{a \to -\infty} \int_a^t x'(\tau) \,d\tau [/itex]
  4. Sep 18, 2011 #3
    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. ><

    Last edited: Sep 18, 2011
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