Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises: 44

Answer

\[2 - \pi \]

Work Step by Step

\[\begin{gathered} \int_{ - \pi /2}^{\pi /2} {\left( {\cos x - 1} \right)} dx \hfill \\ \hfill \\ {\text{integrating}} \hfill \\ \hfill \\ \left[ {\sin x - x} \right]_{ - \pi /2}^{\pi /2} \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ \left[ {\sin \left( {\frac{\pi }{2}} \right) - \frac{\pi }{2}} \right] - \left[ {\sin \left( { - \frac{\pi }{2}} \right) + \frac{\pi }{2}} \right] \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ 1 - \frac{\pi }{2} + 1 - \frac{\pi }{2} \hfill \\ \hfill \\ 2 - \pi \hfill \\ \end{gathered} \]
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