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Question about laplace transform limits

  1. Aug 21, 2011 #1
    if say the function

    f(t) is 0 from 1 to 2
    is 1 from 2 to 3

    if i laplace transform it , for f(t) = 1, i get f(s) = 1/s

    so what are the limits for my s ? is it still 2 to 3?

    thanks!
     
  2. jcsd
  3. Aug 21, 2011 #2

    HallsofIvy

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    Science Advisor

    No, the Laplace transform of your function is NOT 1/s. That is the Laplace transform of f(x)= 1 for all x.

    In order to have a Laplace transform, a function has to be defined for all non-negative number. It doesn't make any sense to talk about a function that is only defined between 1 and 3 as you have here.

    Instead, let f(x)= 1 for x between 2 and 3 and 0 for all other non-negative x. Then the Laplace transform is
    [tex]\int_0^\infty f(x)e^{-sx}dx= \int_2^3 e^{-sx}dx= \left[\frac{-1}{s}e^{-sx}\right]_2^3[/tex]
    [tex]= \frac{e^{-2s}- e^{-3s}}{s}[/tex]
    and s can have any value. The values of "s" have nothing to do with the values of "x".
     
  4. Aug 21, 2011 #3
    ah thank you very much
     
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