If the area bounded by the parabola y = 2 - x 2 and the line y = - x is k 2 sq. units, then the value of 2 k is equal to

Step-by-step solution

Solving y = 2 - x 2 & y = - x ; we get - x = 2 - x 2 ⇒ x = 2 , - 1 ⇒ A - 1,1   &   B 2 , - 2 Thus, the required area A = ∫ - 1 2 2 - x 2 - - x d x = 2 x - x 3 3 + x 2 2 - 1 2 = 9 2 ⇒ k = 9 ∴ 2 k = 1 8