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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