Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises: 38



Work Step by Step

$\int^1_0 cosh (t) dt$ The first step is to integrate cosh(t). (Remember that $\int^b_a cosh(x)dx = sinh(x)|^b_a$ and $sinh(x) = \frac{e^x - e^{-x}}{2}$): $= [sinh(t)]|^1_0$ $= (\frac{e^t - e^{-t}}{2})|^1_0$ Next step is to plug in the limits of integration and simplify until final answer is reached: $= (\frac{e^1-e^{-1}}{2}) - (\frac{e^0 - e^0}{2})$ $= \frac{e - \frac{1}{e}}{2} - 0$ $= \frac{\frac{e^2 - 1}{e}}{2}$ $= \frac{e^2 - 1}{2e}$
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