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KVPY2018MathematicsDefinite Integration

The value of the integral ∫ 0 π 1 - | sin 8 x | d x is

Options

  1. A0
  2. Bπ - 1
  3. Cπ - 2
  4. Dπ - 3

Correct answer

C. π - 2

Step-by-step solution

Let I = ∫ 0 π 1 - | sin 8 x | d x I = ∫ 0 π d x - ∫ 0 π | sin 8 x | d x I = π - ∫ 0 π 8 × 8 | sin 8 x | d x I = π - 8 ∫ 0 π 8 sin 8 x d x [ ∵ sin 8 x B periodic with π 8 ] I = π - 8 - cos 8 x 8 0 π / 8 I = π + cos π - cos 0 = π - 2

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