Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 7 - Section 7.2 - Trigonometric Integrals - 7.2 Exercises - Page 485: 65

Answer

$\displaystyle{s=-\frac{1}{3w}\cos^3wt+\frac{1}{3w}}$

Work Step by Step

$\displaystyle{s=\int f(t)\ dt}\\ \displaystyle{s=\int \sin wt\ \cos^2wt\ dt}\\ \displaystyle{s=-\frac{1}{3w}\cos^3wt+C}$ $\displaystyle{s=-\frac{1}{3w}\cos^3wt+\frac{1}{3w}}$ $s=f(0)=0\\$ $0=-\frac{1}{3w}\cos^3w(0)+C\\ 0=-\frac{1}{3w}+C\\ C=\frac{1}{3w}\\$ $\displaystyle{s=-\frac{1}{3w}\cos^3wt+\frac{1}{3w}}$
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