University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.2 - Volumes Using Cylindrical Shells - Exercises - Page 363: 12

Answer

$$14 \pi $$

Work Step by Step

Consider the shell model to compute the volume: $$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\=\int_1^{4} (2 \pi) \cdot (x)[\dfrac{3}{2 \sqrt x}] dx \\=3 \pi \times \dfrac{x^{3/2}}{\frac{3}{2}}|_{1}^{4} \\=14 \pi $$
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