Polar area element
= Polar area element
{title2=$dA=r\,dr\,d\theta$}
For <polar coordinates> $x=r\cos\theta$, $y=r\sin\theta$ with $r\geq0$, the <Jacobian determinant> is $r$. The <change of variables formula> therefore gives the <area element> $dA=r\,dr\,d\theta$. Integrating over the radial interval $r_1(\theta)\leq r\leq r_2(\theta)$ gives $[r_2(\theta)^2-r_1(\theta)^2]/2$ per unit angle. Bounds must describe the intended region without counting it more than once.