Find the area enclosed by the curve y = – x2 and the straight line x + y + 2 = 0

To find region enclosed by

y = – x2 ...(i)


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


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


x – x2 + 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 = – x2 and the straight line x + y + 2 = 0 is


28