Answer :

As the curves bound the area as shown in figure.

Point of intersection can be obtained as –

As y = x and y = x^{2}

∴ x^{2} = x

⇒ x^{2} – x = 0

⇒ x(x – 1) = 0

⇒ x = 0 or x = 1

Therefore intersection points are (0,0) and (1,1).

Required area = area of ΔOAB – area of curve OCBA

=

=

∴ The area of the region bounded by the parabola y = x^{2} and y = x is 1/6 sq units.

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