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MHT CET2018MathematicsDefinite Integration

∫ 0 π 4 x . sec 2 ⁡ x d x =

Options

  1. Aπ 4 + log ⁡ 2
  2. Bπ 4 - log ⁡ 2
  3. C1 + log ⁡ 2
  4. D1 - 1 2 log ⁡ 2

Correct answer

B. π 4 - log ⁡ 2

Step-by-step solution

Integrating by parts ∫ 0 π 4 x sec 2 x d x = ( x ∫ sec 2 x d x ) 0 π 4 − ∫ 0 π 4 ( d d x ( x ) . ∫ sec 2 x d x ) d x = ( x tan x ) 0 π 4 − ∫ 0 π 4 tan x d x ⇒ I = x tan x - ℓ n sec x 0 π 4 = π 4 1 - ℓ n 2 = π 4 - log 2

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