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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

Consider the integral I n = ∫ 0 π 4 sin 2 n − 1 x sin x d x , then the value of I 20 - I 19 is

Options

  1. A1 20
  2. B- 1 19
  3. C- 1 25
  4. D1 19

Correct answer

B. - 1 19

Step-by-step solution

I 20 − I 19 = ∫ 0 π 4 sin 39 x − sin 37 x sin   x d x ⇒ I 20 − I 19 = ∫ 0 π 4 2 sin   x   cos 38 x sin   x d x = sin 38 x 19 π 4 0 = sin 38 π 4 19 = - 1 19

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