Answer
See the answer below.
Work Step by Step
The region $E$ can be expressed as:
$E = (r,\theta) | {h_1(\theta ) \leq r \leq h_2 (\theta ), \alpha \leq y \leq\ \beta }$
We have $\iint_{D} dA$ as the area of the region $D$.
Apply the polar coordinates $x=r \cos \theta, y= r \sin \theta$ to write $dA$ as: $dA= r \ dr d \theta $
Now, $\iint_{E} f(x,y) \ dA=\int_{\alpha}^{\beta} \int_{h_1(\theta ) }^{h_2(\theta ) } r f(r \cos \theta, r \sin \theta) \ dr \ d \theta$
