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

are sometimes called the moments of inertia of the body about the -plane, plans, and -plane respectively.

   
  Practice Exercises
(1)
 Compute the area bounded by the lines and
  Answer
   
(2)
 Find the volume of the solid whose base is the region in the -plane bounded by the parabola
  and the line and whose top is bounded by the plane
  Answer
   
(3)
 Find the volume common to the cylinders and using double integral over a region
  in the plane. (Hint: Consider the part in the first octant.)
  Answer
   
(4)

Find the total mass of a solid for which the density is given:

(i)
is the cylinder .
(ii)
 , is the solid tetrahedron with vertices .
  Answer
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