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JEE Main2009MathematicsDefinite IntegrationActual

₀^ [ x] d x,[ ] denotes the greatest integer function, is equal to

Options

  1. A2
  2. B1
  3. C-1
  4. D- 2

Correct answer

D. - 2

Step-by-step solution

aligned & Let I = ₀^ [ x] d x & = ₀^ [ ( -x)] d x= ₀^ [- x] d x aligned Adding (1) and (2) aligned & 2 I= ₀^ [ x] d x+ ₀^ [- x] d x== ₀^ (-1) d x [ [x]+[-x]=-1 if x Z & =[-x]₀^ =- & I=- 2 aligned

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