Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 9 - Further Applications of the Integral and Taylor Polynomials - Chapter Review Exercises - Page 496: 7



Work Step by Step

Given $$ y=x+1, \quad[0,4]$$ \begin{align*} y'&= 1\\ 1+y'^2&= 2 \end{align*} Then the surface area is given by \begin{align*} S&=2\pi \int_{a}^{b} y\sqrt{1+y'^2}dx\\ &=2\pi \int_{0}^{4}\sqrt{2}(x+1)dx\\ &=\sqrt{2}\pi (x+1)^2 \bigg|_{0}^{4}\\ &=24\sqrt{2}\pi \end{align*}
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