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NDA 2019 Maths · Mathematics · Definite Integrals · easy

If [x] denotes the greatest integer not exceeding x, then ∫0^3[x] dx is equal to

Single correct option

If [x][x] denotes the greatest integer not exceeding xx, then ∫03[x] dx\displaystyle\int_0^3[x]\,dx is equal to
  1. A. 33
  2. B. 66
  3. C. 92\frac92
  4. D. 22
Show answer and solution

Answer: (A) 33

On [0,1)[0,1) the integrand is 00, on [1,2)[1,2) it is 11 and on [2,3)[2,3) it is 22. The integral is 0⋅1+1⋅1+2⋅1=30\cdot1+1\cdot1+2\cdot1=3. The value 92\frac92 is ∫03x dx\int_0^3x\,dx, which ignores the step nature of [x][x].
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Original question written in the NDA 2019 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