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 271: 10


a) $x^{\frac{1}{2}}+C$ b) $x^{\frac{-1}{2}}+C$ c) $ x^{\frac{-3}{2}}+C$

Work Step by Step

a) The anti-derivative is: $\dfrac{1}{2}\dfrac{x^{-1/2+1}}{-1/2+1}+C=x^{\frac{1}{2}}+C$ b) The anti-derivative is: $\dfrac{-1}{2}\dfrac{x^{-3/2+1}}{-3/2+1}+C=x^{\frac{-1}{2}}+C$ c) The anti-derivative is: $\dfrac{-3}{2}\dfrac{x^{-5/2+1}}{-5/2+1}+C= x^{\frac{-3}{2}}+C$
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