Question

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

Answer 1

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 (2, 4) and C(-1, 1)

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 \(\frac{9}{2}\) sq. units.