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## Triple integrals in cylindrical coordinates.

Example 7.16   Let be the cylinder whose equation is (x-1)2+y2=4. By substitution from  2.5, we have:

i.e., an equation for in cylindrical coordinates is the following:

Example 7.17   Let be the cylinder whose equation is (x-2)2+y2=4. By substitution from  2.5, we have:

i.e., an equation for in cylindrical coordinates is the following:

Example 7.18   Compute the volume of the domain enclosed by the xy-plane, the cylinder whose equation is x2+y2=1 and the paraboloid whose equation is z=4-x2-y2.

The coordinates inequalities for the given domain are:

We have:

Example 7.19   Compute the volume of the domain enclosed by the paraboloids P1 and P2 whose respective equations are z=x2+y2 and z=4-x2-y2.

The coordinates inequalities for the given domain are:

The two paraboloids intersect for z=2, i.e. . We have:

Next: Triple integrals in spherical Up: Triple integrals. Previous: Applications: masses, moments, center
Noah Dana-Picard
2001-05-30