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in Integrals calculus by (41.3k points)

Let C1 and C2 be the graphs of the function y = x2 and y = 2x, 0 ≤ x ≤ 1 respectively. Let C3 be the graph of a function y = f(x); 0 ≤ x ≤ 1, f(0) = 0. For a point P on C1, let the lines through P parallel to the axis, meet C2 and C3 at Q and R, respectively (see Fig.). If for every position of P on (C1), the areas of shaded region OPQ and ORP are equal, determine the function f(x).

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by (41.5k points)
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Best answer

See Fig.

On the curve C1, that is, y = x2 

Let P be (αα2). Hence, ordinate of point Q on C2 is also α2

Now on C2(y = 2x) the abscissa of Q is given by x = y/2 = α2/2.

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