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Manipal MET2014MathematicsDefinite Integration

₀^ 3 2 [ 2 x ] d x , where [ ] denotes the greatest integer function, is equal to

Options

  1. A2 ( 1+ 1)
  2. B2 ( 1+ 2)
  3. C2 ( 1- 1)
  4. D2 ( + 2)

Correct answer

B. 2 ( 1+ 2)

Step-by-step solution

aligned & ₀^ 3 2 ( 2 x ) d x= ₀^ 2 ( 2 x ) d x+ _ 2 ^ ( 2 x ) d x & + _ ^ 3 2 ( 2 x ) d x & =0+ 1 _ 2 ^ d x+ 2 _ ^ 3 2 d x & aligned = 2 ( 1+ 2)

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