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The area of the region bounded by the parabola y = x2 + 1 and the straight line x + y = 3 is given by
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)