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JEE Main202226 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual

∫ 0 20 π sin x + cos x 2 d x is equal to:

Options

  1. A10 π + 4
  2. B10 π + 2
  3. C20 π - 2
  4. D20 π + 2

Correct answer

D. 20 π + 2

Step-by-step solution

Let I = ∫ 0 20 π sin x + cos x 2 d x We know that the period of sin x + cos x is π 2 i.e. I = 40 ∫ 0 π 2 sin x + cos x 2 d x I = 40 ∫ 0 π 2 1 + sin 2 x d x = 40 x - cos 2 x 2 0 π 2 = 40 π 2 - cosπ 2 + cos 0 2 I = 20 π + 2

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