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 - 15.7 Exercises - Page 1049: 4

Answer

$\dfrac{5}{8}$

Work Step by Step

Here, we have $ \int_{0}^1 \int_{x}^{2x} \int_{0}^{y} 2xyz dz dx dy= \int_{0}^1 \int_{x}^{2x} |xyz^2|_{0}^{y} dx dy$ or, $=\int_{0}^1\int_x^{2x} xy^3 dy dx$ $=\int^{0}_{1}(\dfrac{xy^4}{4}]_x^{2x}dx$ or, $=\dfrac{15}{4}\int_0^1 x^5 dx$ or, $=[\dfrac{15}{4}(x^6/6)]_0^1$ or, $=\dfrac{5}{8}$
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