Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 16 - Multiple Integration - 16.3 Triple Integrals - Exercises - Page 870: 6

Answer

$16 \ln (3)$

Work Step by Step

Given: $ f(x, y, z)=\dfrac{z}{x}$ The iterated triple integral can be calculated as: $\iiint_{\mathcal{B}} f(x,y,z)d V = \iiint_{\mathcal{B}} \dfrac{z}{x} d V \\ =\int_{1}^{3} \int_{0}^{2} \int_{0}^{4} [\dfrac{z}{x}] \ dz dy \ dx \\ = \int_{1}^{3} \int_{0}^{2} [\dfrac{z^2}{2x}]_0^4 \ dy \ dx\\=\int_{1}^{3} \int_0^2 \dfrac{8}{x} \ dy \ dx \\=\int_1^3 [\dfrac{8y}{x}]_0^2 \ dx \\=\int_1^3 (\dfrac{16}{x}) \ dx \\=16 [\ln |x|]_1^3 \\=16 [\ln (3) -\ln (1)] \\=16 \ln (3)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.