Q24 of 45 Page 1

Find the area of the region bounded by the parabola y = x2 and y = x.


As the curves bound the area as shown in figure.


Point of intersection can be obtained as –


As y = x and y = x2


∴ x2 = x


⇒ x2 – 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 = x2 and y = x is 1/6 sq units.


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