Given f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩x,0≤x<1212x=121−x12<x<1 and g(x)=(x−12)2,x∈R. Then the area (in sq. units) of the region bounded by the curves y=f(x) and y=g(x) between the lines 2x=1 to 2x=√3 is:

Given f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩x,0≤x<

1.	Given f(x)=⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩x,0≤x<1212x=121−x12<x<1 and g(x)=(x−12)2,x∈R. Then the area (in sq. units) of the region bounded by the curves y=f(x) and y=g(x) between the lines 2x=1 to 2x=√3 is:
Answer» Given $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} x, & 0 \leq x < \frac{1}{2} \frac{1}{2} & x = \frac{1}{2} 1 - x & \frac{1}{2} < x < 1 \end{matrix}$ and $g (x) = {(x - \frac{1}{2})}^{2}, x \in R$ . Then the area (in sq. units) of the region bounded by the curves $y = f (x)$ and $y = g (x)$ between the lines $2 x = 1$ to $2 x = \sqrt{3}$ is: