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 280: 49


$$f(x)=1+\cos x$$

Work Step by Step

Given: Slope$=-\sin x$ and passes through $(0,2)$ The curve is given by \begin{align*} f(x)&=\int (-\sin x)dx\\ &=\cos x+c \end{align*} Since the curve passes through $(0,2)$, then $c=1$ and $$f(x)=1+\cos x$$
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