Question: Let (t) be a function defined for all positive values of t. The Laplace Transform of (t) is defined by when the improper integral exists.

Let ƒ(t) be a function defined for all positive values of t. The Laplace Transform of ƒ(t) is defined by

8 Sr 0 F(s): = e-stf(t) dt

when the improper integral exists. Laplace Transforms are used to solve differential equations. In Exercises find the Laplace Transform of the function.

ƒ(t) = t

8 Sr 0 F(s): = e-stf(t) dt

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