Thomas' Calculus 13th Edition

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

Chapter 6: Applications of Definite Integrals - Practice Exercises - Page 363: 21

Answer

$\dfrac{28 \sqrt 2 \pi }{3}$

Work Step by Step

Integrate the integral to calculate the surface area as follows: Surface area, $S=2\pi \int_{c}^{d}(y) \sqrt {1+(\dfrac{dy}{dx})^2}$ or, $ =2 \pi \int_{0}^{3} \sqrt {2x+1} \sqrt {\dfrac{2x+2}{2x+1}} dx$ or, $=2 \sqrt 2 \pi \times (\dfrac{2}{3}) \times (8-1)$ or, $= \dfrac{28 \sqrt 2 \pi }{3}$
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