Solution
= Solution
For <polar coordinates>, $x=r\cos\theta$ and $y=r\sin\theta$. The <Jacobian determinant> is $r$, so the <area element> is
$$
\boxed{dS=r\,dr\,d\theta\qquad(r\ge0).}
$$
This accounts for the increasing length of an angular strip as its distance from the origin increases.