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: 42

Answer

\[\pi - 2\]

Work Step by Step

\[\begin{gathered} \int_0^\pi {\left( {1 - \sin x} \right)} dx \hfill \\ \hfill \\ {\text{Integrate}} \hfill \\ \hfill \\ = \left[ {x + \cos x} \right]_0^\pi \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ = \left[ {\pi + \cos \pi } \right] - \left[ {0 + \cos 0} \right] \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ \left( {\pi - 1} \right) - \left( {0 + 1} \right) \hfill \\ \hfill \\ Therefore \hfill \\ \hfill \\ \pi - 1 - 1 \hfill \\ \hfill \\ \pi - 2 \hfill \\ \end{gathered} \]
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