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JEE Main20231 Feb 2023Evening ShiftMathematicsDefinite IntegrationActual

The value of the integral ∫ - π 4 π 4 x + π 4 2 - cos 2 x d x is :

Options

  1. Aπ 2 6
  2. Bπ 2 12 3
  3. Cπ 2 3 3
  4. Dπ 2 6 3

Correct answer

D. π 2 6 3

Step-by-step solution

Let, I = ∫ - π 4 π 4 x + π 4 2 - cos 2 x d x                   … 1 Now replacing x → - x we get, ⇒ I = ∫ - π 4 π 4 - x + π 4 2 - cos 2 x d x                     … 2 Now both the equation we get, ⇒ 2 I = ∫ - π 4 π 4 π 2 2 - cos 2 x d x ⇒ I = π 4 · 2 ∫ 0 π 4 d x 2 - cos 2 x d x   as   cos 2 x &#1

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