Answer
$$s(t) = 2+\sin t$$
Work Step by Step
Given $v(t) =\cos t$ , $s(0)=2$
Since
\begin{align*}
s'(t)&=v(t)\\
s(t)&=\int v(t)dt\\
&=\int \cos t dt\\
&=\sin t+c
\end{align*}
Since $s(0)=2 $, then $c=2 $, and
$$s(t) = 2+\sin t$$
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 4 - Integration - 4.2 The Indefinite Integral - Exercises Set 4.2 - Page 279: 42
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