Answer
$\frac{1}{s(s^2+4)}$
Work Step by Step
Given: $f(t)=\int^t_0 (t-\omega)\cos 2\omega d\omega$
Using the Convolution Theorem
$L[f(s)]=L[f*g]\\
=L[f].L(g)\\
=L[t].L[\cos 2t]\\
=\frac{1}{s^2}.\frac{s}{s^2+4}\\
=\frac{1}{s(s^2+4)}$
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 - 10.10 Chapter Review - Additional Problems - Page 718: 18
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