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

Hence, the required volume is

This, as computed earlier, the volume isunits.

   
41.2.7 Note(Some physical applications):
(i)

Average of a function over a region :

 

Let be integrable over . Then

is called the average of over . Similarly if is integrable, then

 

is called the average of over .

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