Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Practice Exercises - Page 933: 26



Work Step by Step

$$I=\int_{1}^{e} \int_{1}^{x} \int_{0}^{z} (\dfrac{2y}{z^3}) \ dy \ dz \ dx \\=\int_{1}^{e} \int_{1}^{x} z^{-1} \ dz \ dx \\=\int_{1}^{e} [\ln (x)] \ dx \\=[ x \ln x -x]_1^e \\=(e-1) \times (\ln e -\ln 1) - (e-1) \\=1-0 \\=1$$
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