Answer
$\frac{\sqrt{3}}{8}$
Work Step by Step
\begin{aligned}
\int_{0}^{\pi / 3} \sin ^{2} x \cos x d x&=\frac{1}{3}\sin^3x\bigg|_0^{\pi/3}\\
&= \frac{1}{3}\sin^3(\pi/3)-\frac{1}{3}\sin(0)\\
&=\frac{\sqrt{3}}{8}
\end{aligned}
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 320: 38
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