If the area of the region x , y : x 2 - 2 ≤ y ≤ x is A , then 6 A + 16 2 is equal to ______________

Step-by-step solution

Given, x 2 - 2 ≤ y   &   y ≤ x Now on finding the intersection point we get, x , y ≡ 1 , 1   &   2 , 2 Now plotting the curve of the above function we get, Now from above diagram required bounded area will be, A = ∫ 1 2 x - 2 - x 2 d x + ∫ 2 2 x - x 2 - 2 d x ⇒ A = x 2 2 - 2 x + x 3 3 1 2 + x 2 2 - x 3 3 + 2 x 2 2 ⇒ A = 1 - 2 2 + 2 2 3 - 1 2 - 2 + 1 3 + 2 - 8 3 + 4 - 1 - 2 2 3 + 2 2 ⇒ A = 9 2 - 8 2 3 ⇒ 6 A = 27 - 16 2 ⇒  &#