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JEE Main201910 Apr 2019Morning ShiftMathematicsDefinite IntegrationActual

The value of ∫ 0 2 π sin ⁡ 2 x 1 + cos ⁡ 3 x d x , where [ t ] denotes the greatest integer function is

Options

  1. Aπ
  2. B2 π
  3. C- π
  4. D- 2 π

Correct answer

C. - π

Step-by-step solution

I = ∫ 0 2 π sin 2 x 1 + cos 3 x d x       … 1 I = ∫ 0 2 π sin 2 π - 2 x 1 + cos 2 π - 3 x d x Applying ∫ 0 a f x = ∫ 0 a f a - x d x I = ∫ 0 2 π - sin 2 x 1 + cos 3 x d x     … 2 Adding 1 and 2 2 I = ∫ 0 2 π sin ⁡ 2 x 1 + cos ⁡ 3 x + - sin ⁡ 2 x 1 + cos ⁡ 3 x d x ⇒   2 I = ∫ 0 2 π - 1 d x       ∵     x + - x = 0       : x &

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