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: 64

Answer

$$2{e^u} + 3u + 6$$

Work Step by Step

$$\eqalign{ & f\left( u \right) = 2{e^u} + 3 \cr & {\text{find an antiderivative of }}f\left( u \right) \cr & F\left( u \right) = 2{e^u} + 3u + C \cr & {\text{using the initial condition }}F\left( 0 \right) = 8 \cr & 8 = 2{e^0} + 3\left( 0 \right) + C \cr & 8 = 2\left( 1 \right) + 3\left( 0 \right) + C \cr & 8 = 2 + C \cr & 8 - 2 = C \cr & C = 6 \cr & {\text{then}} \cr & = 2{e^u} + 3u + 6 \cr} $$
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