# Nasty areas - 2

Calculus Level pending

Let $\displaystyle{f(x) = max\{x^2 , (1-x)^2 , 2x(1-x)}\}$,where$$\displaystyle{0 \le x \le 1}$$. The area of the region bounded by the curves $y=f(x),x-axis,x=0,x=1$ can be expressed as $$\dfrac{a}{b}$$ . Give $$\displaystyle{a+b}$$

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