Q38 of 123 Page 22

Find the area of the region enclosed by the parabola x2 = y and the line y = x + 2.

To Find the area of the region enclosed by

x2 = y …(i)


y = x + 2 …(ii)


On solving the equation (i) and (ii),


Or x2 – x – 2 = 0


Or (x – 2) (x + 1) = 0


Or x = 2 or x = – 1


∴y = 4 or y = 1


Points of intersection are A () and C


These are shown in the graph below: -



Area of the bounded region






The area of the region enclosed by the parabola x2 = y and the line y = x + 2 is


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