$$\iint\limits_{\Bbb R} f(x,y) dA=\iint\limits_{\Bbb R} f(r \cos \theta,r \sin \theta) r\space dr \space d\theta$$
How do we prove that formula, My lecturer said that one of the ways is using the approach of pie circle formula $A = \frac12 \cdot\Delta\theta\cdot r^2$
What I know is $y = r \sin \theta$, $x = r \cos \theta$, and $x^2 + y^2 = r^2$