imo class 12 definite integration

Evaluate ∫[0 to π] |cos x| dx.

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#IMO#Class 12#Mathematics#Definite Integration#logical-reasoning

Evaluate ∫[0 to π] |cos x| dx.

  • A. 0
  • B. 1
  • C. 2
  • D. π

Answer: C) 2

Explanation: cos x is positive in [0, π/2] and negative in [π/2, π]. So, ∫[0 to π/2] cos x dx - ∫[π/2 to π] cos x dx = [sin x] from 0 to π/2 - [sin x] from π/2 to π = (1 - 0) - (0 - 1) = 2.

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