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JEE Main202313 Apr 2023Evening ShiftMathematicsDefinite IntegrationActual

The value of e - π 4 + ∫ 0 π 4 e - x tan 50 x d x ∫ 0 π 4 e - x ( tan 49 x + tan 51 x ) d x

Options

  1. A51
  2. B50
  3. C25
  4. D49

Correct answer

B. 50

Step-by-step solution

Let, I = e - π 4 + ∫ 0 π 4 e - x tan   50 x d x ∫ 0 π 4 e - x tan 49 x + tan 51 x d x Now let I 1 = ∫ 0 π 4 e - x ( tan 49 x + tan 51 x ) d x Now solving, I 2 = ∫ 0 π 4 e - x tan 50 x d x using byparts we get, I 2 = ∫ 0 π 4 e - x tan 50 x d x ⇒ I 2 = - e - x tan 50 x 0 π 4 - ∫ 0 π 4 50 tan 49 x sec 2 x - e - x d x ⇒ I 2 = - e - π 4 + ∫ 0 π 4 50 tan 49 x 1 + tan 2 x e - x d x ⇒ I 2 = - e - π 4 + 50

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