Module 14 :  Double Integrals, Applilcations to Areas and Volumes Change of variables
Lecture 41 :  Applications of multiple integrals  [Section 41.2]
 

Since, the solid has projection onto -plane to be

the required volume is

41 .2.3 Example:
 

Find the volume of the region enclosed between the two surfaces

.

The two surfaces intersect on the cylinder


The region projects onto the region in the -plane enclosed by the ellipse having the same equation. Thus,


Hence, by Fubini's theorem, the required volume is

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