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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