Find the area of the region bounded by the curves y² = x and y = x.

Model Answer & Options

Source: Extra Practice

1/6 sq. units

1/3 sq. units

1/2 sq. units

2/3 sq. units

Explanation

The curves intersect where x² = x, so x = 0 and x = 1. In the interval [0, 1], √x ≥ x. Area = ∫[0 to 1] (√x - x) dx = [2/3 x^(3/2) - x²/2] from 0 to 1 = 2/3 - 1/2 = 1/6. Option B is just the integral of √x, and option C is just the integral of x; option D is a common error in power rule application.

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