Calculus, 10th Edition (Anton)

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


$$s(t) = 2t^{3/2}-15$$

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 $$s(t) = 2t^{3/2}-15$$
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