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: 74

Answer

$(\dfrac{-1}{\pi}) \cot (\pi s)+c$

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 $\int \csc^2 x =-\cot t+C$ Plug $\pi s =a $ and $\pi ds=da$ $\int \csc^2 a (\dfrac{1}{\pi}) da=(\dfrac{1}{\pi}) \int \csc^2 (a) da$ or, $(\dfrac{1}{\pi}) \int \csc^2 (a) da=(\dfrac{-1}{\pi}) \cot (a)+c$ Hence, $(\dfrac{-1}{\pi}) \cot (a)+c=(\dfrac{-1}{\pi}) \cot (\pi s)+c$
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