Calculus (3rd Edition)

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

Chapter 6 - Applications of the Integral - Chapter Review Exercises - Page 320: 43


$c \pi$

Work Step by Step

The Washer method to compute the volume of revolution: When the function $f(x)$ is continuous and $f(x) \geq g(x) \geq 0$ on the interval $[m,n]$, then the volume of a solid obtained by rotating the region under $y=f(x)$ over an interval $[m,n]$ about the x-axis is given by: $V=\pi \int_{m}^{n} (R^2_{outside}-R^2_{inside}) \ dy$ where, $R_{outside}=\sqrt {1+x^2}$ and $ R_{inside}=x$ Now, $V=\pi \int_0^c [(\sqrt {1+x^2})^2 -(x)^2] \ dx \\ = \pi \int_0^c (1+x^2-x^2) \ dx \\=\pi [ x]_0^c \ dx \\=\pi (c-0) \\=c \pi$
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