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Homework Help: Help show that Laplace transform exists

  1. Mar 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that f(t)=e^(5t) sin(t) satisfies the condition for the LaPlace transform to exist

    I can solve the Laplace and get 2/((s-5)^2 + 4)

    How do I show that the conditions exist? If it is solvable using the table, shouldn't that be enough?
  2. jcsd
  3. Mar 24, 2009 #2


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    Science Advisor
    Gold Member

    You must show that the improper integral defining the Laplace transform of the function exists. Recall that you define the value of an improper integral as the limit of a regular definite integral as the limit of integration approaches the singular value (in this case the upper limit of integration approaching infinity).
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