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MHT CET2017MathematicsDefinite Integration

If ∫ 0 π 2 log ⁡ cos ⁡ x d x = π 2 log ⁡ 1 2 , then ∫ 0 π 2 log ⁡ sec ⁡ x d x =

Options

  1. Aπ 2 log ⁡ 1 2
  2. B1 - π 2 log ⁡ 1 2
  3. C1 + π 2 log ⁡ 1 2
  4. Dπ 2 log ⁡ 2

Correct answer

D. π 2 log ⁡ 2

Step-by-step solution

∫ 0 π 2 log ⁡ sec ⁡ x d x = ∫ 0 π 2 log ⁡ 1 cos ⁡ x d x = - ∫ 0 π 2 log ⁡ ( cos ⁡ x ) d x = - π 2 log ( 1 2 ) = π 2 log 2

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