Chapter 17 Section 17.8 Cylindrical Coordinates

x y z r The point of using different coordinate systems is to make the equations of certain curves much simpler (at least from a calculus perspective). x y z x y z x y z x y z x y z 1 4

x y z This is very useful for the descriptions of cones since they involve a square root which is difficult to deal with in terms of integrals. x y z x y z x y z x y z x y z x y z x y z Some other well known shapes:

Integrating Factor (don’t forget) x y z x y 2

z y x y x 12 Project into xy -plane.

To evaluate the mass integral: