The area (in sq. units) enclosed between the curve x = 1 - t 2 1 + t 2 ,   y = 2 t 1 + t 2 ,   ∀ t ∈ R and the line y = x + 1 above the line is

Step-by-step solution

Let, t = tan ⁡ θ ⇒ x = cos ⁡ 2 θ ,   y = sin ⁡ 2 θ ⇒ x 2 + y 2 = 1 Area of the shaded region = π 4 - 1 2 × 1 × 1 = π 4 - 1 2 sq. units