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KVPY2020MathematicsDefinite Integration

The value of the integral ∫ - π / 2 π / 2 sin 2 x 1 + e x d x is

Options

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

Correct answer

B. π 4

Step-by-step solution

I = ∫ 0 π / 2 sin 2 x 1 + e x + sin 2 x 1 + e - x d x = ∫ 0 π / 2 sin 2 x d x = 1 2 × π 2 = π 4

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