Find the volume (in units3) of the solid generated by revolving the region bounded by the curve y = ln(x), the x-axis, and the vertical line x = e4 about the x-axis

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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Find the volume (in units3) of the solid generated by revolving the region bounded by the curve y = ln(x), the x-axis, and the vertical line x = e4 about the x-axis.

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Step 1

Method of finding the volume of the solid generated by revolving the region bounded by the curve and the x axis axb, about the x-axis is as follows.

V=πabfx2dx

The region of revolution is as below.

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