Answer
See below
Work Step by Step
We are given: $f(t)=e^t\\
g(t)=e^t \sin t$
Obtain: $(f * g)=\int^t_0f(t-x)g(x)dx\\
=\int^t_0 e^{t-x} e^x \sin xdx\\
=e^t \int^t_0 \sin xdx\\
=\begin{bmatrix}
-e^t \cos x
\end{bmatrix}^t_0\\
=e^t (1-\cos t)$
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: 6
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