Module 14 : Double Integrals, Applilcations to Areas and Volumes Change of variables
Lecture 41 : Triple integrals [Section 41.1]
These are called the iterated integrals with respect to the projection of onto the -plane. In all it may be possible to express a triple integral in six iterated integral, corresponding to projections of onto the three coordinate planes. Regions which can be projected onto a coordinate plane are called elementary regions
41.1.4
Examples:
(i)
Let us compute
where is the solid in bounded by the ellipsoid
We can interpret as
where is the projection of onto -plane.
onto the 
-plane. In all it may be possible to express a triple integral in six iterated integral, corresponding to projections of 
onto the three coordinate planes. Regions 
which can be projected onto a coordinate plane are called elementary regions
is the solid in 
bounded by the ellipsoid 
as 
is the projection of 
onto 
-plane. 
and its projection in 
-plane 
