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The integral I = ∫ π 4 π 2 sin 6 ⁡ x d x satisfies

Options

  1. AI > π 2
  2. BI > π 4
  3. CI ∈ π 4 , π 2
  4. DI ∈ π 32 , π 4

Correct answer

D. I ∈ π 32 , π 4

Step-by-step solution

∫ π 4 π 2 sin 6 ⁡ π 4 d x < ∫ π 4 π 2 sin 6 ⁡ x d x < ∫ π 4 π 2 sin 6 ⁡ π 2 d x ⇒ 1 8 ∫ π 4 π 2 d x < I < ∫ π 4 π 2 d x ⇒ 1 8 ⋅ π 4 < I < π 4 or I ∈ π 32 , π 4

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