Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.9 - Antiderivatives - 4.9 Exercises: 35

Answer

$F(x) = 3x^{5/3} - 75$

Work Step by Step

$F(x) = \int 5x^{2/3} + C$ $F(x) = \int 5(\frac{3}{5}x^{5/3} + C)$ $F(x) = 3x^{5/3} + C$ Given $f(8) = 21$: $F(8) = 3(8)^{5/3} + C$ $F(8) = 3(32) + C$ $21 = 96 + C$ $C = -75$ $F(x) = 3x^{5/3} - 75$
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