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: 42


$$s(t) = 2+\sin t$$

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 $$s(t) = 2+\sin t$$
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