The area bounded by y = 2 – x^2 and x + y = 0 is A. 7/2 sq. units

Question

The area bounded by y = 2 – x² and x + y = 0 is

A. \(\frac{7}{2}\) sq. units

B. \(\frac{9}{2}\) sq. units

C. 9 sq. units

D. None of these

Answer 1

Correct answer is B.

- 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 –