Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - 5.5 Substitution Rule - 5.5 Exercises: 24

Answer

\[ = \frac{{\,{{\left( {\sin \theta } \right)}^{11}}}}{{11}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{{\sin }^{10}}\theta \cos \theta dx} \hfill \\ \hfill \\ set\,\,the\,\,substitution \hfill \\ \hfill \\ u = \sin \theta \,\,\,\,\,\,\,\,then\,\,\,\,\,\,\,du = \cos \theta d\theta \hfill \\ \hfill \\ apply\,\,the\,\,\,substitution \hfill \\ \hfill \\ \int_{}^{} {{{\sin }^{10}}\theta \cos \theta dx} = \int_{}^{} {{u^{10}}du} \hfill \\ \hfill \\ integrate\,\, \hfill \\ \hfill \\ = \frac{{{u^{11}}}}{{11}} + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,\,u = \sin \theta \hfill \\ \hfill \\ = \frac{{\,{{\left( {\sin \theta } \right)}^{11}}}}{{11}} + C \hfill \\ \hfill \\ \end{gathered} \]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.