University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Practice Exercises - Page 343: 90


$$\int^{3\pi/4}_{\pi/4}\csc z\cot zdz=0$$

Work Step by Step

$$A=\int^{3\pi/4}_{\pi/4}\csc z\cot zdz$$ $$A=-\csc z\Big]^{3\pi/4}_{\pi/4}=-\frac{1}{\sin z}\Big]^{3\pi/4}_{\pi/4}$$ $$A=-\Big(\frac{1}{\sin(3\pi/4)}-\frac{1}{\sin(\pi/4)}\Big)$$ $$A=-\Big(\frac{1}{\frac{\sqrt2}{2}}-\frac{1}{\frac{\sqrt2}{2}}\Big)$$ $$A=0$$
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