Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises: 59

Answer

$$\frac{{{x^6}}}{6} + \frac{2}{x} + x - \frac{{19}}{6}$$

Work Step by Step

$$\eqalign{ & f\left( x \right) = {x^5} - 2{x^{ - 2}} + 1 \cr & {\text{find an antiderivative of }}f\left( x \right),{\text{ use power rule}} \cr & F\left( x \right) = \frac{{{x^6}}}{6} - 2\left( {\frac{{{x^{ - 1}}}}{{ - 1}}} \right) + x + C \cr & F\left( x \right) = \frac{{{x^6}}}{6} + 2{x^{ - 1}} + x + C \cr & {\text{using the initial condition }}F\left( 1 \right) = 0 \cr & 0 = \frac{{{{\left( 1 \right)}^6}}}{6} + 2{\left( 1 \right)^{ - 1}} + 1 + C \cr & {\text{then}} \cr & C = - \frac{{19}}{6} \cr & {\text{so}}{\text{,}} \cr & = \frac{{{x^6}}}{6} + 2{x^{ - 1}} + x - \frac{{19}}{6} \cr & = \frac{{{x^6}}}{6} + \frac{2}{x} + x - \frac{{19}}{6} \cr} $$
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