Module 14 :  Double Integrals, Applilcations to Areas and Volumes Change of variables
Lecture 41 :  Applications of multiple integrals  [Section 41.2]
41 .2 Applications of Multiple integrals
41.2.1 Definition :
 

Let be a closed bounded region.

(i)
 If the double integral
 


Then is called the area of the region .

(ii)
 Let be a solid in which has projection in -plane and is bounded above by the surface
  and below by -plane. If the double integral
 


then is called the volume of the solid .

41.2.2 Examples :
(i)

Let us find the area bounded by the graphs of the functions
 
 
           Figure: Area between and
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