multiple integrals Flashcards
1
Q
what is x in spherical polar coordinates
A
x = rsinθcosφ
2
Q
what is y in spherical polar coordinates
A
y = rsinθsinφ
3
Q
what is z in spherical polar coordinates
A
x = rcosθ
4
Q
what angles do θ and φ represent in spherical polar coordinates
A
θ is the angle from the positive z axis
φ is the angle from the positive x axis
5
Q
what are the ranges of θ and φ for spherical polar coordinates
A
0 <= θ < π
and - π < φ < π
6
Q
what is the volume element, dxdydz, converted into spherical polar coordinates
A
dxdydz = r^2 (sinθ)^2 drdθdφ
7
Q
what is the area element, dxdy, in polar coordinates
A
dxdy = r drdθ
