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: 5


$$\dfrac{14 \pi }{3}$$

Work Step by Step

Consider the shell model to compute the volume: $$V=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\ = \int_0^{\sqrt 3} (2 \pi) \cdot (x)[\sqrt {x^2+1}) dx $$ Let us consider $a=x^2+1 $ and $da=2xdx$ $$Volume= \pi \times \int_1^{4} \sqrt a da \\ =\pi \times [\dfrac{2}{3})a^{5/2}]_1^4 \\=\dfrac{14 \pi }{3}$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.