Answer
$\int_{0}^{\pi}\int_{2}^{4}f(r, \theta), r dr d\theta$
Work Step by Step
Using polar co-ordinates, we can define the region $R$ as follows:
$R=(r,\theta) | 2\leq r\leq 4, 0\leq \theta \leq \pi$
Therefore,
${\int\int}_{R}f(x,y)dA=\int_{0}^{\pi}\int_{2}^{4}f(r, \theta), r dr d\theta$
