The area (in sq. units) of the region, given by the set x , y ∈ R × R ∣ x ≥ 0 , 2 x 2 ≤ y ≤ 4 - 2 x is :

Step-by-step solution

Given curves are y = 2 x 2   &   y = 4 - 2 x So, 2 x 2 = 4 - 2 x ⇒ 2 x 2 + 2 x - 4 = 0 ⇒ x - 1 x + 2 = 0 So, the x -coordinate of the intersection point is 1 as x = - 2 < 0 Required area ∫ 0 1 4 - 2 x - 2 x 2 d x = 4 x - x 2 - 2 x 3 3 0 1 = 4 - 1 - 2 3 = 7 3