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Find the area of the region bounded by the two parabolas y = x2 and y2 = x.

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The point of intersection of these two parabolas are O (0, 0) and A (1, 1) as shown in the fig.

Here, we can set y2 = x  or y = √x = f(x) (because region lies above x-axis) and y = x2 = g(x) where, f(x) ≥ g(x) in [0, 1].

Therefore, the required area of the shaded region

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