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99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration

∫ 0 π 2 sin x sin x + cos x + e x d x = π 4 + 1 2 log 2 1 + e x then x is equal to

Options

  1. Aπ 4
  2. Bπ 8
  3. Cπ 2
  4. Dπ

Correct answer

C. π 2

Step-by-step solution

I = ∫ 0 π 2 sin x sin x + cos x + e x d x = 1 2   ∫ 0 π 2 sin x   + cos x + e x - - sin x + cos x + e x sin x + cos x + e x d x So, I =   1 2   ∫ 0 π 2 1 . d x - 1 2 log sin x + cos x + e x 0 π 2 ⇒ I = π 4 + 1 2 log 1 + e π 2 2 = π 4 - 1 2 log 2 1 + e π 2 Comparing we get, x = π 2

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