The maximum possible area bounded by the parabola y = x 2 + x + 10 and a chord of the parabola of length 1 is

Step-by-step solution

We have, y = x 2 + x + 10 ⇒ x 2 + x + 1 4 = y - 10 + 1 4 ⇒ x + 1 2 2 = y - 39 4 Latusrectum of parabola is 1 . ∴ Length of chord is also 1 . Area is maximum when chord is latusrectum. Area of shaded region = Area of rectangle O A B C - 2 ∫ - 1 / 2 0 parabola = 10 - 2 ∫ - 1 2 0 x 2 + x + 10 d x = 10 - 2 x 3 3 + x 2 2 + 10 - 1 2 0 = 10 - 2 - 1 24 + 1 8 - 10 2 = 1 6