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KVPY2014MathematicsDefinite Integration

For a real number x let [x] denote the largest integer less than or equal to x and x =x-[x] . Let n be a positive integer. Then ₀^ n (2 [x] x ) d x is equal to :

Options

  1. A0
  2. B1
  3. Cn
  4. D2 n-1

Correct answer

C. n

Step-by-step solution

₀^ n (2 [x] x y )n ₀¹ (2 [x] 1 d x)=n ₀¹ d x=n

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