imo class 12 definite integration

Evaluate ∫[0 to π/4] tan²x dx.

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Evaluate ∫[0 to π/4] tan²x dx.

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

Answer: A) 1 - π/4

Explanation: Use the identity tan²x = sec²x - 1. Integral becomes ∫(sec²x - 1) dx = [tan x - x]. Evaluating from 0 to π/4 gives (1 - π/4) - (0 - 0) = 1 - π/4.

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