If the area of the region ( x , y ) : 0 ≤ y ≤ min 2 x , 6 x - x 2 is A , then 12 A is equal to _______.

Step-by-step solution

Solving, y = 2 x and y = 6 x - x 2 ⇒ 2 x = 6 x - x 2 ⇒ 4 x - x 2 = 0 ⇒ x 4 - x = 0 ⇒ x = 0 , 4 ⇒ y = 0 , 8 ⇒ x , y ≡ 0 , 0 , 4 , 8 So, the required area is given by, A = 1 2 × 4 × 8 + ∫ 4 6 6 x - x 2 dx ⇒ A = 16 + 3 x 2 - x 3 3 4 6 ⇒ A = 76 3 ⇒ 12 A = 304