Answer
$\frac{\pi}{6}$
Work Step by Step
$V$ = ${\pi}\int_0^{\frac{1}{a}}a^{2}(x-ax^{2})dx$
$V$ = ${\pi}(\frac{1}{2}a^{2}x^{2}-\frac{1}{3}a^{3}x^{3})|_0^{\frac{1}{a}}$
$V$ = $\frac{\pi}{6}$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 6 - Applications of the Integral - Chapter Review Exercises - Page 320: 46
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