Find the area enclosed by the curve y = – x^{2} and the straight line x + y + 2 = 0

To find region enclosed by

y = – x^{2} ...(i)

x + y + 2 = 0 ...(ii)

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

x – x^{2} + 2 = 0

Or x = 2 or – 1

∴y = – 4, – 1

Equation (i) represents a parabola opening towards the negative y - axis.

Equation (ii) represents a line passing through ( – 2,0) and (0, – 2).

Their points of intersection A( – 1, – 1) and B(2, – 4).

These are shown in the graph below: -

Area of the bounded region

The area enclosed by the curve y = – x^{2} and the straight line x + y + 2 = 0 is

28