Mathematics - Area Under Curves Question with Solution | TestHub

Let ${\mathrm{C}}_1\&{\mathrm{C}}_2$ be the graphs of the functions $\mathrm{y}={\mathrm{x}}^2\&\mathrm{y}=2\mathrm{x},0\le \mathrm{x}\le 1$ respectively. Let ${\mathrm{C}}_3$ be the graph of a function $\mathrm{y}=\mathrm{f}(\mathrm{x}),0\le \mathrm{x}\le 1,\mathrm{f}(0)=0$. For a point P on ${\mathrm{C}}_1$, let the lines through P, parallel to the axes, meet ${\mathrm{C}}_2\&{\mathrm{C}}_3$ at Q & R respectively (see figure). If for every position of P (on ${\mathrm{C}}_1$ ), the areas of the shaded regions OPQ & ORP are equal, determine the function f (x).