Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 4: Applications of Derivatives - Practice Exercises - Page 245: 76

Answer

$3 \sec (\dfrac{\theta}{3})+c$

Work Step by Step

Use formula $\int x^{a} dx=\dfrac{x^{a+1}}{n+1}+c$ where $c$ is a constant of proportionality. As we know that $\int \sec x \tan x =\sec x+C$ Plug $\dfrac{\theta}{3}=a$ and $da=(\dfrac{1}{3}) d \theta$ Then, $3 \int \sec k \tan k+c=3 \sec a+c$ Hence, $3 \sec (a)=3 \sec (\dfrac{\theta}{3})+c$
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