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Laplace transform help

  1. Mar 22, 2012 #1
    1. The problem statement, all variables and given/known data
    We have been given a table of laplace transforms and have been asked to show them using the definition. ∫0e-stf(t)dt.

    But this one I have no clue where to begin
    0tf(t)dt the laplace transform of this is F(s)/s.
    Can anyone tell me what to do with this one? Thank you in advance.


    2. Relevant equations

    0e-stf(t)dt

    0tf(t)dt transforms to F(s)/s

    3. The attempt at a solution

    I have it set up as
    0[∫0tf(t)dt]e-stdt
     
  2. jcsd
  3. Mar 22, 2012 #2
    Sorry I know it is difficult to read with the superscripts and subscripts. I didn't know a better way of displaying it.
     
  4. Mar 22, 2012 #3

    HallsofIvy

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    Yes, that's correct. Now do the integral using integration by parts
    Let "u" be [itex]\int_0^t f(t)dt[/itex]. What is du?
    Let "dv" be [itex]e^{-st}dt[/itex]. What is v?
     
  5. Mar 22, 2012 #4
    Check out the first part of the fundamental theorem of calculus, and think of that integral with the upper limit as t as some function.
     
  6. Mar 22, 2012 #5
    Ok so du would be f(t)?
    and v would be -1/s e-st
     
  7. Mar 22, 2012 #6
    That's right!
     
  8. Mar 23, 2012 #7
    Im sorry but im still having trouble with one. Can you help me with how to proceed?
     
  9. Mar 23, 2012 #8
    I have it written out as uv - ∫vdu, but I dont know how to go from there.
     
  10. Mar 23, 2012 #9
    Try to prove the simpler but related problem using integration by parts, then you'll have some clue:
    L{g'(t)}=sG(s)-g(0).
    Then let g(t)=∫ _{0 to t} f(τ)dτ
     
  11. Mar 23, 2012 #10
    thank you HallsofIvy, QuarkCharmer, and sunjin09.
     
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