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Let C1 and C2, be the graph of the func...

Let `C_1 and C_2`, be the graph of the functions `y= x^2 and y= 2x, 0<=x<= 1` respectively. Let `C_3`, be the graph of a function `y- (fx), 0<=x<=1, f(0)=0`. For a point Pand `C_2`, let the lines through P, parallel to the axes, meet `C_2 and C_3`, at Q and R respectively. If for every position of P (on `C_1`), the areas of the shaded regions `OPQ and ORP` are equal, determine the function `f(x)`.

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