Laplace Transform

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  • #1
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Homework Statement
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?
 
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Answers and Replies

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

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.
 
  • #3
vela
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Just doing this in my head, but I think the second integral evaluates to log(5/2).
 
  • #4
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I forgot to change the limits of integration when I used the method of substitution.
 

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