Given: f(x)= {x, 0 ≤ x<1/2; 1/2, x=1/2; 1-x, 1/2<x ≤ 1} and g (x)=(x-1/2)^2, x ∈ R. Then the area (in sq. units) of the region bounded by the curves,…

Given : $\displaystyle f(x)= \begin{cases}x & , 0 \leq x<\frac{1}{2} \\ \frac{1}{2} & , x=\frac{1}{2} \\ 1-x & , \frac{1}{2}<x \leq 1\end{cases}$ and $\displaystyle \mathrm{g}(x)=\left(x-\frac{1}{2}\right)^2, x \in \mathbf{R}$. Then the area (in sq. units) of the region bounded by the curves, $\displaystyle y=f(x)$ and $\displaystyle y=g(x)$ between the lines, $\displaystyle 2 x=1$ and $\displaystyle 2 x=\sqrt{3}$, is :