Thomas' Calculus 13th Edition

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

Chapter 15: Multiple Integrals - Section 15.5 - Triple Integrals in Rectangular Coordinates - Exercises 15.5 - Page 900: 9

Answer

6

Work Step by Step

$\int^e_1 \int^{e^2}_1 \int^{e^3}_1 \frac{1}{xyz}$ dx dy dz =$\int^e_1 \int^{e^2}_1 [\frac{ln x}{yz}]^{e^3}_1 dy $ dz =$\int^e_1 \int^{e^2}_1 \frac{3}{yz}$ dy dz =$3 \int^e_1 [\frac{ln y}{z}]^{e^2}_1$ dz =$\int^e_1 \frac{6}{z}$ dz =6
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