Multivariate Calculus - Bruce E. Shapiro

Lecture 18
Double Integrals in Polar
Coordinates
Recall that in polar coordinates the point P = (x, y) is represented by the numbers:
r, the distance of P from the origin; and
θ, the angle, measured counter-clockwise from the axis
between the x-axis and the line segment from the origin to P.
Figure 18.1: The point P is represented by the cartesian coordinates (x, y) and the
polar coordinates (r, θ).
To convert from Cartesian coordinates to polar coordinates,
x = r cos θ
y = r sin θ
To convert from polar coordinates to Cartesian coordinates,
r 2 = x 2 + y 2
tan θ = y/x
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