Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 28


$$ \frac{-1}{499}\cos^{499}y+\frac{1}{501}\cos^{501}+c$$

Work Step by Step

\begin{align*} \int \cos ^{498} y \sin ^{3} y d y&=\int \cos ^{498} y \sin ^{2} y\sin y d y\\ &=\int \cos^{498}y(1-\cos^2 y)\sin ydy\\ &= \int (\cos^{498}y-\cos^{500} y)\sin ydy\\ &=\frac{-1}{499}\cos^{499}y+\frac{1}{501}\cos^{501}+c \end{align*}
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.