Module 14 :  Double Integrals, Applilcations to Areas and Volumes Change of variables
Lecture 41 :  Triple integrals  [Section 41.1]
 

Hence

For further, computation, if treat as a type-II region, then

 
  Practice Exercises
(1)

For the following integrals, sketch the region of integration and express the integral in six iterated integrals:

(i)
, where is the solid in in the first octant bounded by the coordinate planes, the plane
  and the vertical plane .
(ii)
  where is the solid in is the paraboloid cylinder bounded on the side by the paraboloid , top by the plane and the bottom by the - plane.
  Answers
8