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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

The value of the definite integral I = ∫ ln ⁡ 3 2 ln ⁡ 2 3 ln ⁡ 2 - tan 7 ⁡ x 2 + tan 7 ⁡ x d x is equal to

Options

  1. Aln ⁡ 4
  2. Bln ⁡ 2
  3. C0
  4. Dln ⁡ 1 2

Correct answer

C. 0

Step-by-step solution

If f x = ln ⁡ 2 - tan 7 ⁡ x 2 + tan 7 ⁡ x , then f - x = ln ⁡ 2 + tan 7 ⁡ x 2 - tan 7 ⁡ x = - ln ⁡ 2 - tan 7 ⁡ x 2 + tan 7 ⁡ x = - f x So, f x is an odd function Hence, ∫ ln ⁡ 3 2 ln ⁡ 2 3 f x d x = 0

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