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Average value of a function of two variables

Jacobian for dV (rectangular)
dx dy dz


Average value of a function of three variables

Convert the following to polar coordinates
x
y
 x=rcos(Θ)
 y=rsin(Θ)

What is the jacobian for dA (polar)?
dA = r dr dθ

What is the jacobian for dV (cylindrical)?
dV = r dz dr dθ

Convert the following from rectangular to cylindrical coordinates
x
y
z

Convert from cylindrical coordinates to rectangular coordinates
z
r
θ

Convert from rectangular coordinates to spherical coordinates
x
y
z
 x=ρcosθsinφ
 y=ρsinθsinφ
 z=ρcosφ

Convert from spherical to rectangular coordinates
ρ
φ
θ

What is the jacobian for dV in spherical coordinates

What is the change of variables formula for double integrals?

What is the change of variables formula for triple integrals?

