Let the area of the region ( x , y ) : 0 ≤ x ≤ 3 , 0 ≤ y ≤ min x 2 + 2 , 2 x + 2 be A . Then 12 A is equal to ______.

Step-by-step solution

Given, 0 ≤ y ≤ min x 2 + 2 , 2 x + 2 , x ∈ 0 , 3 Now, plotting the diagram of the above expression we get, Now, from above diagram we get, A = ∫ 0 2 x 2 + 2 d x + ∫ 2 3 2 x + 2 d x ⇒ A = x 3 3 + 2 x 0 2 + x 2 + 2 x 2 3 ⇒ A = 8 3 + 4 + 9 + 6 - 4 - 4 ⇒ A = 20 3 + 7 = 41 3 ⇒ 12 A = 164