Answer
$$2\pi ab-\pi b^2$$
Work Step by Step
We know the following equation for the area of the shaded region:
$$ A_{shaded}=\text{Overall Area} - \text{ Area Used Up}$$
Using this, we find:
$$ \pi a^2 - \pi (a-b)^2 \\ \pi a^2-\pi \left(a^2-2ab+b^2\right) \\ 2\pi ab-\pi b^2$$