Given \( f(x)=\left\{\begin{array}{cc}x, & 0 \leq x\frac{1}{2} \\ \...
Given \( f(x)=\left\{\begin{array}{cc}x, & 0 \leq x\frac{1}{2} \\ \frac{1}{2}, & x=\frac{1}{2} \\ 1-x, & \frac{1}{2}x \leq 1\end{array}\right. \) and \( g(x)=\left(x-\frac{1}{2}\right)^{2} \)
\( \mathrm{P} \) \( \mathrm{x} \in \mathrm{R} \). Then the area (in sq. units) of the region bounded by the curves, \( \mathrm{y}=\mathrm{f}(\mathrm{x}) \) and \( \mathrm{y}=\mathrm{g}(\mathrm{x}) \) between the lines, \( 2 x=1 \) and \( 2 x=\sqrt{3} \), is :
[JEE Main-2020 (January)]
(a) \( \frac{1}{2}-\frac{\sqrt{3}}{4} \)
(b) \( \frac{1}{3}+\frac{\sqrt{3}}{4} \)
(c) \( \frac{1}{2}+\frac{\sqrt{3}}{4} \)
(d) \( \frac{\sqrt{3}}{4}-\frac{1}{3} \)
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