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JEE Main202622 January 2026Morning ShiftMathematicsDefinite IntegrationActual

The value of _ - 2 ^ 2 ( 1 [x]+4 ) d x , where [ ] denotes the greatest integer function, is

Options

  1. A1 60 (21 -1)
  2. B7 60 ( -3)
  3. C7 60 (3 -1)
  4. D1 60 ( -7)

Correct answer

C. 7 60 (3 -1)

Step-by-step solution

I = _ - /2 ^ /2 1 [x] + 4 , dx I = _ - /2 ⁻¹ dx 2 + _ -1 ⁰ dx 3 + ₀¹ dx 4 + ₁^ /2 dx 5 = 1 2 (-1 + 2 ) + 1 3 (1) + 1 4 (1) + 1 5 ( 2 - 1 ) = 7 20 - 7 60 = 7 60 (3 - 1)

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