Math 210 Lecture 13: Triple integrals in
cylindrical and spherical coordinates
Daniel Ingebretson
University of Illinois at Chicago
July 10, 2024
,Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
,Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
Polar coordinates (r , θ) in the xy -plane, and Cartesian
coordinate z along the z-axis.
, Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
Polar coordinates (r , θ) in the xy -plane, and Cartesian
coordinate z along the z-axis.
Conversion:
y
r 2 = x 2 + y 2, x = r cos θ, y = r sin θ, tan θ = .
x
cylindrical and spherical coordinates
Daniel Ingebretson
University of Illinois at Chicago
July 10, 2024
,Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
,Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
Polar coordinates (r , θ) in the xy -plane, and Cartesian
coordinate z along the z-axis.
, Cylindrical coordinates (r , θ, z)
Cylindrical coordinates are (r , θ, z).
Polar coordinates (r , θ) in the xy -plane, and Cartesian
coordinate z along the z-axis.
Conversion:
y
r 2 = x 2 + y 2, x = r cos θ, y = r sin θ, tan θ = .
x
