Answered: Find the volume of a solid obtained by…

Find the volume of a solid obtained by rotating the region underneath the graph of f(x) = 24 - 6x² about the y-axis over the interval [0, 2]. (Use symbolic notation and fractions where needed.)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

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Question

Find the volume of a solid obtained by rotating the region underneath the graph of f(x) = 24 - 6x² about the y-axis over the
interval [0, 2].
(Use symbolic notation and fractions where needed.)

Expert Solution

Step 1

To find the volume of a solid obtained by rotating the region underneath the graph of

$f (x) = 24 - 6 x^{2}$ about the $y$ -axis over the interval $[0, 2]$ .

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