The area bounded by the curve y = x 2 - 9 and the line y = 3 is

Step-by-step solution

We first find the points of intersection of the curves y = x 2 - 9 and y = 3 which gives, x 2 - 9 = 3 ⇒ x 2 - 9 = ± 3 ⇒ x 2 = 12 (or) x 2 = 6 ⇒ x = ± 12 (or) x = ± 6 The graphs of the two curves are shown in figure We have to find the area of the shaded region. Required area = 2 A 1 + 2 A 2 ( ∵ The areas A 1 & A 2 are symmetrical about y - axis ) where A 1 = ∫ 0 6 9 - x 2 − 3 d x A 1 = ∫ 0 6 6 - x 2 d x = 6 x - x 3 3 0 6 = 6 6 - 6 6 3 = 12 6 3 = 4 6 A 2 = &#8