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Let f(x)= maximum {x^2, (1-x)^2, 2x(1 - ...

Let `f(x)=` maximum `{x^2, (1-x)^2, 2x(1 - x)}` where `x in [0, 1].` Determine the area of the region bounded by the curve `y=f(x)` and the lines `y = 0,x=0, x=1.`

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`(17)/(27)` sq. units
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