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MHT CET2017MathematicsDefinite Integration

∫ 0 3 x d x = _ _ _ _ _ _ , where [ x ] is greatest integer function

Options

  1. A3
  2. B0
  3. C2
  4. D1

Correct answer

A. 3

Step-by-step solution

∫ 0 3 x d x = ∫ 0 1 0 d x + ∫ 1 2 1 d x + ∫ 2 3 2 d x = x 1 2 + 2 x 2 3 = 2 - 1 + 2 3 - 2 = 1 + 2 = 3

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