?The Laplace Transform If is continuous for , the Laplace transform of is the function

Chapter 7, Problem 85

(choose chapter or problem)

The Laplace Transform If $f(t)$ is continuous for $t⩾0$ , the Laplace transform of $f$ is the function $F$ defined by

$F(s)=\int\limits_{0}^{\infty{}} f(t){e}^{-st}dt$

and the domain of $F$ is the set consisting of all numbers $s$ for which the integral converges.

Find the Laplace transform of each of the following functions.
(a) $f(t)=1$
(b) $f(t)={e}^{t}$
(c) $f(t)=t$

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