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+1 vote
11.2k views
in Mathematics by (88.9k points)

Let Cand C2 be the graphs of functions 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 axes, meet C2 and 

C3 at Q and R respectively (see figure). If for every position of P(on C1) the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).

1 Answer

+2 votes
by (79.0k points)
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Best answer

Refer to the Fig. in the question. Let the coordinates of P be (x, x2), where ≤ x ≤ 1.

For the area (OPRO), upper boundary y = x2

lower boundary : y = f(x)

lower limit of x : 0

upper limit of x : x

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