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 901: 20


$8 \ln 2$

Work Step by Step

$\int^7_0 \int^2_0 \int^{\sqrt{4-q^2}}_0 \frac{q}{r+1}$ dp dq dr =$\int^7_0 \int^2_0 \frac{q\sqrt{4-q^2}}{r+1}$ dq dr =$\int^7_0 \frac{1}{3(r+1)}[-(4-q^2)^{3/2}]^2_0$ dr =$\frac{8}{3} \int^7_0 \frac{1}{r+1}dr $ =$\frac{8 \ln 8}{3}$ =$8 \ln 2$
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