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KVPY2014MathematicsSequences and Series

For a real number x let [x] denote the largest integer less than or equal to x . The smallest positive integer n for which the integral ₁^ n [x][ x ] d x exceeds 60 is

Options

  1. A8
  2. B9
  3. C10
  4. D[60^ 2 / 3 ]

Correct answer

B. 9

Step-by-step solution

₁^ n [x][ x ] d x= ₁^ n 2 d x+ . .= 50 for n=8 66 for n=9

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