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The value of ∫ 0 π 2 cos ⁡ 2 x cos 2 2 ⁡ x cos 2 3 ⁡ x cos ⁡ 2 4 x d x is equal to

Options

  1. A0
  2. B1 2
  3. Cπ 2
  4. Dπ 4

Correct answer

A. 0

Step-by-step solution

Let the value of integral is I , then, Ι = ∫ 0 π 2 cos ⁡ 2 x cos ⁡ 2 2 x cos ⁡ 2 3 x cos ⁡ 2 4 x d x Ι = ∫ 0 π 2 - cos ⁡ 2 x cos ⁡ 2 2 x cos ⁡ 2 3 x cos ⁡ 2 4 x d x (applying f ( x ) = f ( a + b - x ) ) Adding, we get, 2 Ι = 0 ⇒ Ι = 0

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