Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 7 - Applications of Integration - 7.3 Exercises: 17

Answer

$\frac{\pi}{2}$

Work Step by Step

Setup the integration using shell method about the x-axis $ 2\pi \int_{\frac{1}{2}}^1 y(\frac{1}{y} -1)dy + 2\pi \int_0^{\frac{1}{2}} ydy$ $ 2\pi \int_{\frac{1}{2}}^1 (1-y)dy + 2\pi \int_0^{\frac{1}{2}}y dy$ , Integrate $ 2\pi(y-\frac{1}{2}y^2)]^1_{\frac{1}{2}} + \pi(y^2)]_0^{\frac{1}{2}}$, Take definite integral $ 2\pi ((1-\frac{1}{2})-(\frac{3}{8})) + \pi(\frac{1}{4})$, Simplify $ \frac{\pi}{4} + \frac{\pi}{4}$ $\frac{\pi}{2}$
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