The area bounded by y = 1 - x 2 and y = x 3 - x is divided by y -axis in the ratio λ : 1 ∀ λ > 1 , then λ is equal to

Step-by-step solution

From the figure, λ 1 = ∫ 0 1 1 - x 2 - x 3 - x d x ∫ - 1 0 1 - x 2 - x 3 - x d x ⇒ λ = sin - 1 x - x 4 4 + x 2 2 0 1 sin - 1 x - x 4 4 + x 2 2 - 1 0 = π 4 - 1 4 - 1 2 π 4 - - 1 4 + 1 2 = π + 1 π - 1