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JEE Main202126 Feb 2021Morning ShiftMathematicsDefinite IntegrationActual

The value of ∫ - π / 2 π / 2 cos 2 x 1 + 3 x d x is:

Options

  1. Aπ 2
  2. Bπ 4
  3. C2 π
  4. D4 π

Correct answer

B. π 4

Step-by-step solution

Given I = ∫ - π / 2 π / 2 cos 2 x 1 + 3 x d x     . . . i Using ∫ a b f x d x = ∫ a b f a + b - x d x , we get I = ∫ - π / 2 π / 2 cos 2 x 1 + 3 - x d x = ∫ - π / 2 π / 2 3 x cos 2 x 1 + 3 x d x     . . . i i Adding i   &   i i we get, 2 I = ∫ - π / 2 π / 2 1 + 3 x cos 2 x 1 + 3 x d x 2 I = ∫ - π / 2 π / 2 cos 2 x d x 2 I = 2 ∫ 0 π / 2 cos 2 x d x I = ∫ 0 π / 2 cos 2 x

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