Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.3 Trigonometric Integrals - 7.3 Exercises: 9

Answer

\[ = \frac{x}{2} - \frac{{\sin 2x}}{4} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{{\sin }^2}xdx} \hfill \\ \hfill \\ use\,\,\,{\sin ^2}x = \frac{{1 - \cos 2x}}{2} \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ = \int_{}^{} {{{\sin }^2}xdx} = \int_{}^{} {\,\left( {\frac{{1 - \cos 2x}}{2}} \right)} \,dx \hfill \\ \hfill \\ distribute \hfill \\ \hfill \\ = \int_{}^{} {\frac{1}{2}dx} - \frac{1}{2}\int_{}^{} {\cos 2xdx} \hfill \\ \hfill \\ or \hfill \\ = \frac{1}{2}\int_{}^{} {dx} - \frac{1}{4}\int_{}^{} {\cos 2x\left( 2 \right)dx} \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = \frac{x}{2} - \frac{{\sin 2x}}{4} + C \hfill \\ \end{gathered} \]
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