# Help show that Laplace transform exists

#### bengaltiger14

1. Homework Statement

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?

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#### jambaugh

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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