Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 5 - Review - True-False Quiz - Page 428: 9

Answer

False

Work Step by Step

False. As a counter example, consider $f(x)=5$. We have $\int_a^bf'(x)[f(x)]^4dx=\int_a^b0\cdot 5^4dx=\int_a^b0dx=0$ but $\frac{1}{5}[f(x)]^5+C=\frac{1}{5}\cdot 5^5+C=625+C\neq 0$
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