Let the straight line x = b divide the area enclosed by y = (1 - x)² , y = 0, and x = 0 into two parts R₁(0 ≤ x ≤ b) and R₂(b ≤ x ≤ 1) such that R₁ - R₂ = 1/4. Then b equals?

R₁ = ∫₀ᵇ (1 - x)² dx = [(x - 1)³/3]₀ᵇ = (b - 1)³/3 + 1/3
R₂ = ∫₁ᵇ (1 - x)² dx = [(x - 1)³/3]₁ᵇ = -(b - 1)³/3
Given R₁ - R₂ = 1/4
(b - 1)³/3 + 1/3 - (-(b - 1)³/3) = 1/4
2(b - 1)³/3 + 1/3 = 1/4
2(b - 1)³/3 = 1/4 - 1/3 = -1/12
(b - 1)³/3 = -1/24
(b - 1)³ = -1/8
(b - 1) = -1/2
b = 1 - 1/2 = 1/2