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: 75


$-(\dfrac{1}{\sqrt 2}) \csc (\sqrt 2 \theta )+c$

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 $\int \csc x \cot x =-\csc x+C$ Plug $\sqrt 2 \theta =a $ and $da=(\sqrt 2) d \theta$ $(\dfrac{1}{\sqrt 2}) \int (\csc a) (\cot a) da=-\dfrac{1}{\sqrt 2} \csc (a)+c$ Thus, $-\dfrac{1}{\sqrt 2} \csc (a)+c=-(\dfrac{1}{\sqrt 2}) \csc (\sqrt 2 \theta )+c$
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