Answer
$\pi\ln(10)$
Work Step by Step
$$V=\int_0^3 2\pi x \frac{1}{x^2+1}dx$$
$$V=\pi\int_0^3 \frac{2x}{x^2+1}dx$$
$$V=\pi\int_0^3 \frac{(x^2+1)'}{x^2+1}dx$$
$$V=\pi[\ln(x^2+1)]_0^3=\pi\ln(3^2+1)-\pi\ln(0^2+1)=\pi\ln(10)$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises - Page 438: 86
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