Chapter 7.8, Problem 73E

If $f\left(t\right)$ is continuous for $t\ge 0$, the Laplace transform of ƒ is the function F defined by

$F\left(s\right)={\displaystyle {\int }_0^{\infty }f\left(t\right)e^{-st}}dt$

and the domain of F is the set consisting of all numbers s for which the integral converges. Find the Laplace transforms of the following functions.

(a) $f\left(t\right)=1$

(b) $f\left(t\right)=e^t$

(c) $f\left(t\right)=t$