Answer
$ \dfrac{ 2! e^{-2 s}}{s^3}$
Work Step by Step
We are given that $f(t)= (t-2)^2 u_{2} (t)$
Now,$F(s)=L[(t-2)^2 u_{2} (t)] \\= e^{-2 s} L [t^2]= \dfrac{ 2! e^{-2 s}}{s^3}$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.7 The Second Shifting Theorem - Problems - Page 704: 6
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