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Homework Help: Laplace Transform

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data
    f(t) is a piecewise function:
    {0 0<= t< 1
    {t*exp(2t) t = >1

    2. Relevant equations
    F(s)= L{f(t)}

    3. The attempt at a solution

    F(s)= L{t*exp(2t)}

    for this problem I just took the Laplace Transformer directly from the table which is: n!/ (s-a)^(n+1)

    and after plucking in the relevant number I got:

    Firstly I want to ask, is this correct? And have I missed any steps when setting up this problem?

    Secondly if this is correct and I don't want to use the table to get the formula directly, can someone please show me other methods to come to the same answer.

  2. jcsd
  3. Oct 11, 2012 #2


    User Avatar
    Science Advisor

    What you have is incorrect. That is the Laplace transform of [itex]f(t)= te^{2t}[/itex] which is NOT the same as the function given here.

    Do not know the definition of the Laplace transform? It is
    [tex]F(f)= \int_0^\infty e^{-st}f(t)dt[/tex]

    Integrate that.
    The Laplace transform of this function is
    [tex]\int_1^\infty e^{-st}te^{2t}dt= \int_1^\infty te^{(2- s)t}dt[/tex]
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