Answer
$$s(t) = 2t^{3/2}-15$$
Work Step by Step
Given $v(t) =3\sqrt{t}$ , $s(4)=1$
Since
\begin{align*}
s'(t)&=v(t)\\
s(t)&=\int v(t)dt\\
&=\int3\sqrt{t} dt\\
&= 2t^{3/2}+c
\end{align*}
Since $s(4)=1 $, then $c=-15 $, and
$$s(t) = 2t^{3/2}-15$$
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: 43
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