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: 49

Answer

\[\frac{\pi }{{12}}\]

Work Step by Step

\[\begin{gathered} \int_1^{\sqrt 3 } {\frac{{dx}}{{1 + {x^2}}}} \hfill \\ \hfill \\ {\text{integrating}} \hfill \\ \hfill \\ \int_1^{\sqrt 3 } {\frac{{dx}}{{1 + {x^2}}}} = \left[ {{{\tan }^{ - 1}}x} \right]_1^{\sqrt 3 } \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ {\tan ^{ - 1}}\left( {\sqrt 3 } \right) - {\tan ^{ - 1}}\left( 1 \right) \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ \frac{\pi }{3} - \frac{\pi }{4} \hfill \\ \hfill \\ \frac{\pi }{{12}} \hfill \\ \end{gathered} \]
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