Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 334: 44


$r=\ln|\tan t+1|+4$ When C=$4, $the graph passes through $(\pi, 4)$

Work Step by Step

$r=\displaystyle \int\frac{\sec^{2}t}{\tan t+1}dt$ $\left[\begin{array}{l} u=\tan t+1\\ du=\sec^{2}tdt \end{array}\right]$ $r=\displaystyle \int\frac{1}{u}du=\ln|u|+C$ $r=\ln|\tan t+1|+C$ $(\pi, 4) $is on the graph, so we find C $4=\ln|0+1|+C$ $C=4$ $r=\ln|\tan t+1|+4$
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