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The value of the integral Ι = ∫ 0 π sin ⁡ x + cos ⁡ x d x , (where . denotes the greatest integer function) is equal to

Options

  1. A1
  2. B2
  3. Cπ
  4. D2 π

Correct answer

C. π

Step-by-step solution

Let, y = sin ⁡ x + cos ⁡ x ⇒ y 2 = 1 + s i n 2 x ∈ 1,2 ⇒ y ∈ 1 , 2 ⇒ sin ⁡ x + cos ⁡ x = 1 Thus, Ι = ∫ 0 π 1 · d x = π - 0 = π

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