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: 63

Answer

$$2{x^4} + 2{x^{ - 1}} + 1$$

Work Step by Step

$$\eqalign{ & f\left( x \right) = 8{x^3} - 2{x^{ - 2}} \cr & {\text{find an antiderivative of }}f\left( x \right),{\text{ use power rule}} \cr & F\left( x \right) = 2{x^4} + 2{x^{ - 1}} + C \cr & {\text{using the initial condition }}F\left( 1 \right) = 5 \cr & 5 = 2{\left( 1 \right)^4} + 2{\left( 1 \right)^{ - 1}} + C \cr & {\text{then}} \cr & 5 = 2 + 2 + C \cr & C = 1 \cr & {\text{so}}{\text{,}} \cr & = 2{x^4} + 2{x^{ - 1}} + 1 \cr} $$
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