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MHT CET202619 April 2026Morning ShiftMathematicsDefinite IntegrationActual

The value of ₂^4 ( x + [x]) ,dx = ...(where x and [x] are the fractional part function and the greatest integer function, respectively)

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

C. 6

Step-by-step solution

By the definition of the fractional part and greatest integer functions, x = [x] + x . Substituting this into the integral: ₂^4 ( x + [x]) ,dx = ₂^4 x ,dx Evaluating the definite integral: ₂^4 x ,dx = [ x^2 2 ]₂^4 = 16 2 - 4 2 = 8 - 2 = 6 Answer: 6

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