imo class 12 definite integration

Evaluate ∫[0 to 1] 1/√(1 - x²) dx.

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Evaluate ∫[0 to 1] 1/√(1 - x²) dx.

  • A. π
  • B. π/4
  • C. 1
  • D. π/2

Answer: D) π/2

Explanation: The anti-derivative is sin⁻¹(x). Evaluating from 0 to 1: sin⁻¹(1) - sin⁻¹(0) = π/2 - 0 = π/2.

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