The area of the region bounded by the parabola y = x 2 + 1 and the straight line x + y = 3 is given by

Question

Philoid · Accepted Answer

The situation looks like this –

At the intersection points, y = 3 – x = x² + 1

Or, x² + x – 2 = 0

⇒ (x + 2)(x – 1) = 0

⇒ x = -2, 1 → these are our bounds

So, area A enclosed is –

A =

=

= 2 – 1/2 - 1/3 + 4 + 2 – 8/3

= 8 – 9/3 – 1/2

= 5 – 1/2

= 9/2 (Ans)