Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - Review Exercises - Page 593: 12

Answer

$$0$$

Work Step by Step

$$\eqalign{ & \int_\pi ^{2\pi } {\cot \frac{x}{3}} dx \cr & = \int_\pi ^{2\pi } {\left( 3 \right)\cot \frac{x}{3}\left( {\frac{1}{3}} \right)} dx \cr & {\text{find the antiderivative}} \cr & = 3\left( {\ln \left| {\sin \frac{x}{3}} \right|} \right)_\pi ^{2\pi } \cr & {\text{evaluate limits}} \cr & = 3\left( {\ln \left| {\sin \frac{{2\pi }}{3}} \right| - \ln \left| {\sin \frac{\pi }{3}} \right|} \right) \cr & {\text{simplify}} \cr & = 3\left( {\ln \left| {\frac{{\sqrt 3 }}{2}} \right| - \ln \left| {\frac{{\sqrt 3 }}{2}} \right|} \right) \cr & = 0 \cr} $$
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.