Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2020 / Paper 1 / 12 / a / Solution

For polar coordinates, $x=r\cos \theta$ and $y=r\sin \theta$. The Jacobian determinant is $r$, so the area element isThis accounts for the increasing length of an angular strip as its distance from the origin increases.