imo class 12 definite integration

Evaluate ∫₀^(π/4) tan² x dx.

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Evaluate ∫₀^(π/4) tan² x dx.

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

Answer: A) 1 − π/4

Explanation: tan² x = sec² x − 1. ∫₀^(π/4) (sec² x − 1) dx = [tan x − x]₀^(π/4) = (1 − π/4) − 0 = 1 − π/4.

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