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WZ
Numerade Educator

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Problem 73 Hard Difficulty

If $ f(t) $ is continuous for $ t \ge 0 $, the Laplace transform of $ f $ is the function $ F $ defined by
$$ F(s) = \int_0^\infty f(t) e^{-st}\ dt $$
and the domain of $ F $ is the set consisting of all numbers s for which the integral converges. Find the Laplace transforms of the following functions.
(a) $ f(t) = 1 $ (b) $ f(t) = e^t $ (c) $ f(t) = t $

Answer

a. $F(s)=\frac{1}{s}$ with domain $\{s | s>0\}$
b. $F(s)=\frac{1}{s-1}$ with domain $\{s | s>1\}$
c. $F(s)=\frac{1}{s^{2}}$ and the domain of $F$ is $\{s | s>0\}$

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Video Transcript

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