imo class 12 definite integration

Evaluate ∫[0 to π/2] (√cot x)/(1 + √cot x) dx.

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Evaluate ∫[0 to π/2] (√cot x)/(1 + √cot x) dx.

  • A. π/4
  • B. π/2
  • C. 0
  • D. 1

Answer: A) π/4

Explanation: Rewriting as ∫ (√cos x)/(√sin x + √cos x) dx. Using the property ∫ f(x) = ∫ f(a-x), and adding to the original integral, we get 2I = π/2, so I = π/4.

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