University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.4 - Areas of Surfaces of Revolution - Exercises - Page 376: 22


$ 4 \pi$

Work Step by Step

The formula to determine the surface area is as follows: $S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2}$ Now, $S =2 \pi \times \int_{0}^{\sqrt 2} (x) \sqrt {1+x^2(x^2+2)} dx \\= 2 \pi [ \dfrac{x^4}{4}+\dfrac{x^2}{2}]_{0}^{\sqrt 2} \\=4 \pi$
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