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JEE Main20199 Jan 2019Morning ShiftMathematicsDefinite IntegrationActual

The value of ∫ 0 π cos x 3 d x is

Options

  1. A2 3
  2. B0
  3. C4 3
  4. D- 4 3

Correct answer

C. 4 3

Step-by-step solution

I = ∫ 0 π cos x 3 d x = 2 ∫ 0 π 2 c o s 3 x d x = 2 ∫ 0 π 2 1 - s i n 2 x c o s x d x = 2 ∫ 0 π 2 c o s x d x - ∫ 0 π 2 s i n 2 x c o s x d x = 2 s i n x - s i n 3 x 3 0 π 2 = 2 1 - 1 3 - 0 + 0 = 4 3

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