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The area bounded by y = 2 – x2 and x + y = 0 is
- the blue shaded region above
To define the bounds, we need to find the points of intersection. We know that at the points of intersection, both the equations are satisfied.
⇒ x + y = 0
⇒ x + (2 – x2) = 0 (from the other equation)
So, x2 – x – 2 = 0 i.e., (x - 2)(x + 1) = 0 or x = -1,2
So, bounds are x = -1 to x = 2
Therefore, area shall be evaluated as –