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

To Find the area of the region enclosed by

x^{2} = y …(i)

y = x + 2 …(ii)

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

Or x^{2} – 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 x^{2} = y and the line y = x + 2 is

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