Question

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)`.

Answer 1

Correct Answer - `f(x) = x^(3) - x^(2)`