Calculate the volume generated by rotating the region bounded by the following curves about each axis. y= In(x)   y=0 ,x=6 y-axis? x axis?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

Calculate the volume generated by rotating the region bounded by the following curves about each axis.

y= In(x)   y=0 ,x=6

y-axis?

x axis?

Expert Solution
Step 1

The volume is found using disk method and washer method .

Disk method : To find the volume of the solid,  first find the cross sectional area of the disk of radius R(x) which is  the distance of the region's boundary from axis of revolution  that is  πR(x)2

Washer method : This is used when the solid generated has a hole in it. The cross sections perpendicular to axis of revolution is washer whose outer radius is R(x) and inner radius is r(x)

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