 
Summary: 15.8 Triple Integrals in Cylindrical and
Spherical Coordinates
We divide this section into two parts. First part deals with the study of triple
integrals in cylindrical coordinates while second part presents the study of
triple integrals in spherical coordinates.
(Part 1)
Triple Integrals in Cylindrical Coordinates
Recall
Cylindrical coordinates: ( ), ,r z
Conversion formulas for cylindrical coordinates
cos , sin ,x r y r z z = = =
Aim: Learn to integrate ( , , )f r z
· Recall area element in polar coordinates: dA rdrd=
· Volume element in cylindrical coordinates dV rdzdrd=
1
Evaluating Triple Integrals in Cylindrical Coordinates
Given a function ( , , )f r z over a solid G such that
is bounded above byG 2 ( , )z g r = and below by 1( , )z g r =
and the projection of G on XYplane is a simple polar region.R
2
