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: 23

Answer

$F(x) = x^5 - \frac{x^{6}}{3} + 4$
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Work Step by Step

$F(x) = \int 5x^4 - 2x^5dx$ $F(x) = \frac{5x^{4+1}}{4+1} - \frac{2x^{5+1}}{5+1} + C$ $F(x) = \frac{5x^{5}}{5} - \frac{2x^{6}}{6} + C$ $F(x) = x^5 - \frac{x^{6}}{3} + C$ $F(0) = 0^5 - \frac{0^{6}}{3} + C$ Given: $F(0) = 4$ $4 = 0 - 0 + C$ $C = 4$ Substitute back the value of C: $F(x) = x^5 - \frac{x^{6}}{3} + C$ $F(x) = x^5 - \frac{x^{6}}{3} + 4$ Graph the function of $f(x)$ and $F(x)$. The graphs make sense -- for instance $f(x)=0$ when $F(x)$ is at a minimum.
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