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JEE Main202225 Jun 2022Morning ShiftMathematicsDefinite IntegrationActual

The value of ∫ 0 π e cos x sin x 1 + cos 2 x e cos x + e - cos x d x is equal to

Options

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

Correct answer

B. π 4

Step-by-step solution

Given I = ∫ 0 π sin x ⋅ e cos x 1 + cos 2 x e cos x + e − cos x d x             . . . i Using property of integral ∫ f a b a + b − x = ∫ a b f x we get I = ∫ 0 π sin x ⋅ e − cos x 1 + cos 2 x e − cos x + e cos x d x             . . . ii Adding equation i & ii we get 2 I = ∫ 0 π sin x 1 + cos 2 x ⋅ e cos x + e − cos x e cos x + e − cos x d x 2 I = ∫ 0 &#

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