Answer
See below
Work Step by Step
Given: $f(t)=t^2\\
g(t)=e^{2t}\sin 2t$
Obtain: $L[f * g]=L[f]L[g]\\
=L[t^2]L[e^{2t} \sin 2t]\\
=\frac{2}{s^3}.\frac{2}{(s-2)^2+4}\\
=\frac{4}{s^3(s-3)^2+4}$
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 - 10.9 The Convolution Integral - Problems - Page 716: 14
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