University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 273: 84

Answer

a) False b) True c) True

Work Step by Step

Differentiate each option to check the original integral: a) We have: $\dfrac{d}{d\theta}[\dfrac{\sec ^3 \theta}{3} +C]= \sec^2 \theta \sec \theta \tan \theta \ne \tan \theta \sec^2 \theta$ b) We have: $\dfrac{d}{d\theta}[\dfrac{1}{2} \tan^2 \theta +C]= \dfrac{1}{2} (2 \sec^2 \theta \tan \theta) = \tan \theta \sec^2 \theta$ c) We have: $\dfrac{d}{d\theta}[\dfrac{1}{2} \sec^2 \theta +C]= \dfrac{1}{2} (2 \sec \theta \sec \theta \tan \theta) = \tan \theta \sec^2 \theta$ Hence, a) False, b) True, c) True
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