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

Let us find the volume of the solid enclosed by the paraboloid

 
 
                        Figure: and its projection in -plane
 

To find the projection of the enclosed solid , we first find the curve of intersection of the two surfaces. This is given by

i.e.,

  Thus, the projection of onto the -plane is given by
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