Module 8 : Applications of Integration - II
Lecture 24 : Volume of solids of revolution by Shell method [Section 24.2]
  about the line . To find its volume by shell method we consider a thin strip of thickness at a point . This strip has height and is at a distance from the axis. Thus, the volume of the thin shell obtained by revolving this strip about is
              

Hence, the required volume is
              
  Visualization of Shell method
 

PRACTICE EXERCISES
1.

Find the volume of the solid of revolution by shell method, when the region enclosed by the given curve is

  revolved about the -axis:
(i)

.
(ii)
.
2.
 Find the volume of the solid of revolution, by shell method, of the region enclosed by the given curves being
revolved about -axis:
(i)
 .
(ii)
 .
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