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Finding the volume of unbounded solids of revolution

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(a) Find the volume of the unbounded solid generated by rotating the unbounded region of y=e^(-x) with x>=1 around the x axis (see the attached figure)
(b) What happens if y=1/sqrt(x) instead?

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Solution Summary

Rotating a bounded portion of the x axis of a graph about the x axis yields "Solids of Revolution". Integration can be used to find the volume of the solids so formed. When the x region is not bounded, we can still perform the rotation to give an *unbounded* solid of revolution. We can attempt to find a volume for this object by first finding the volume of the bounded object in terms of the right hand bound, then trying to take the limit as the right hand bound goes to infinity. This limit may or may not exist. The solution comprises a 1/2 page word attachment with equations written in Mathtype showing two examples of this technique, 1 for which the volume exists and one for which it does not. Step by step explanation is given.

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The volume of the solid of revolution obtained by ...

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