Topic: Engineering Mathematics
Evaluate the integral ∫∫(1-x²)^(-1/2) (1-y²)^(-1/2) dx dy over the region x=0 to 1, y=0 to 1.
- A. π/2
- B. π/4
- C. π²/2
- D. π²/4
Answer: D. π²/4
Explanation: The double integral is separable: [∫(1-x²)^(-1/2) dx] * [∫(1-y²)^(-1/2) dy]. The integral of (1-t²)^(-1/2) is sin⁻¹(t). Evaluating from 0 to 1 gives sin⁻¹(1) - sin⁻¹(0) = π/2. Since both integrals are identical, the result is (π/2) * (π/2) = π²/4.