Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 15 - Review - Exercises - Page 1063: 37

Answer

$$\dfrac{2}{3}$$

Work Step by Step

$$Volume =\int_{0}^{2} \int_{0}^{y} int_0^{(2-y/2)} dz dx dy \\=\int_{0}^{2} \int_{0}^{y} (1-\dfrac{y}{2}) dx dy \\=\\=\int_{0}^{2} \int_{0}^{y} (1-\dfrac{y}{2}) dx dy\\=\int_0^2 y dy - \dfrac{1}{2} \times \int_0^2 y^2 dy\\=\dfrac{2}{3}$$
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