The area (in sq. units) of the region A = ( x , y ) : | x | + | y | ≤ 1 , 2 y 2 ≥ | x |

Step-by-step solution

Required area is, A = ar O A C + ar Δ A B C ⇒ A = 4 ∫ 0 1 / 2 2 y 2 d y + 1 2 · 1 2 · 1 2 ⇒ A = 4 2 3 y 3 0 1 / 2 + 1 8 = 5 6