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Homework Help: Laplace Transform

  1. Jun 22, 2011 #1
    The problem statement, all variables and given/known data
    If [itex]f(t)=K + 2cost[/itex] and F(s) = L{f(t)}, find all the real values of [itex]K[/itex] such that [itex]\int_{1}^{2}F(s)ds = 2ln5[/itex]


    The attempt at a solution
    So L{f(t)} = L{K} + L{2cost} = (K/s) + [2/(s2 + 1)]

    So [tex]\int_{1}^{2}\frac{K}{s}ds + \int_{1}^{2}\frac{2s}{s^{s}+1}ds = 2ln5 [/tex]

    After integration(I used integration by substitution for the second integral) and simplification, I get K(ln2) + ln(2) = 2ln(5)

    Finally, I get K = [ln 25 - ln2]/ln2

    Is this correct?
     
    Last edited: Jun 22, 2011
  2. jcsd
  3. Jun 22, 2011 #2
    The second term in your equation is supposed to be ln(5). Using your method, I get K = 1+ln(5)/ln(2) or ln(10)/ln(2). But I don't see a problem with your method.
     
  4. Jun 22, 2011 #3

    vela

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    Just doing this in my head, but I think the second integral evaluates to log(5/2).
     
  5. Jun 22, 2011 #4
    I forgot to change the limits of integration when I used the method of substitution.
     
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