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Black Book Advanced Problems in MathematicsMathematicsIndefinite and Definite Integration

For each positive integer n , define a function f_n on as follows : f_n(x) = cases 0 & if x = 0 2n & if 0 < x 1 n 2 2n & if 1 n < x 2 n 3 2n & if 2 n < x 3 n & n 2n & if n-1 n < x 1 cases Then the value of _ n ₀^1 f_n(x) dx is :

Options

  1. A2
  2. B1
  3. C2

Correct answer

3

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