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NDA 2023 Maths · Mathematics · Definite Integrals · medium

∫0^3[x] dx, where [x] is the greatest integer function, is equal to

Single correct option

∫03[x] dx\displaystyle\int_0^3[x]\,dx, where [x][x] is the greatest integer function, is equal to
  1. A. 33
  2. B. 92\dfrac92
  3. C. 66
  4. D. 22
Show answer and solution

Answer: (A) 33

On [0,1)[0,1) it is 00, on [1,2)[1,2) it is 11, on [2,3)[2,3) it is 22. The integral is 0+1+2=30+1+2=3. The value 92\dfrac92 is the integral of xx, and 66 is the sum with the wrong upper step.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake