University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Practice Exercises - Page 279: 115



Work Step by Step

Calculate the anti-derivative. Since, we know $\int x^{n} dx=\dfrac{x^{n+1}}{n+1}+c$ and $ \int e^{-x} dx=-e^{-x}+c$ where $c$ is a constant of proportionality. Then $\int (\dfrac{1}{2}e^t-e^{-t}) dt=\int \dfrac{1}{2}e^t dt-\int e^{-t} dt$ As we know $ \int e^{-x} dx=-e^{-x}+c$ or, $= \dfrac{1}{2}e^{t}+e^{-t}+c$
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