2. Use an appropriate method to set up an integral for the volume of the solid formed by rotating the region bounded by y = x³, x = 0, x = 2, y = 0.... (a) around the x-axis. Evaluate this integral. (b) around the y-axis. Evaluate this integral. (c) around the line y = -2. Evaluate this integral.

2. Use an appropriate method to set up an integral for the volume of the solid formed by rotating the region bounded by y = x³, x = 0, x = 2, y = 0.... (a) around the x-axis. Evaluate this integral. (b) around the y-axis. Evaluate this integral. (c) around the line y = -2. Evaluate this integral.

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

2. Use an appropriate method to set up an integral for the volume of the solid formed by rotating the
region bounded by y =x³, x = 0, x = 2, y = 0...
(a) around the x-axis. Evaluate this integral.
(b) around the y-axis. Evaluate this integral.
(c) around the line y = -2. Evaluate this integral.
3. Consider the region enclosed by y = x?+ vã + 1, y = 0, x = 0, and x = 2. This region will be
rotated around the y-axis. Set up the integral to determine the volume using shell method. Evaluate
this integral.

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