The area bounded by the curve y = sin⁻¹ x, x = 0 and x = 1/2 and y = 0 is:

The area bounded by the curve y = sin⁻¹ x, x = 0 and x = 1/2 and y = 0 is:

• A. (π/12 + √3/2 − 1) sq units
• B. (π/12) sq units
• C. (√3/2 − 1) sq units
• D. (π/12 − √3/2 + 1) sq units

Answer: A) (π/12 + √3/2 − 1) sq units

Explanation: Area = ∫[0 to 1/2] sin⁻¹ x dx. Put x = sin θ, dx = cos θ dθ. Limits: 0 to π/6. ∫ θ cos θ dθ = θ sin θ + cos θ. Area = [θ sin θ + cos θ]₀^(π/6) = (π/6)(1/2) + √3/2 − (0+1) = π/12 + √3/2 − 1 sq units.