Question 12
A region on a number plane is enclosed by the x-axis, the y-axis, the line $x=2$ and the graph of the function $y=f(x)$ where
$$f(x)=\begin{cases}1&\text{for }0\le x\le1,\\1+\sqrt{1-(x-2)^2}&\text{for }1\lt x\le2.\end{cases}$$
The area of this region, in square units, is
$$f(x)=\begin{cases}1&\text{for }0\le x\le1,\\1+\sqrt{1-(x-2)^2}&\text{for }1\lt x\le2.\end{cases}$$
The area of this region, in square units, is