Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 15 - Multiple Integrals - Review - Exercises - Page 1075: 33

Answer

$\dfrac{2ma^3}{9}$

Work Step by Step

Consider $Volume=\iint_{R} mx dA$ or, $=\int_{-a/3}^{a/3} \int_0^{\sqrt {a^2-9y^2}} mx dx dy$ or, $=\int_{-a/3}^{a/3} [\dfrac{mx^2}{2}]_0^{\sqrt {a^2-9y^2}} dy$ or, $=m \int_0^{a/3} a^2-9y^2 dy$ or, $=m (a^2 y-3y^3)_0^{a/3}$ or, $=\dfrac{2ma^3}{9}$
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