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Homework Help: Computing the value of an integral from Apostol I

  1. Aug 7, 2010 #1
    1. The problem statement, all variables and given/known data
    The notation [x] denotes the greatest integer <= x

    "integral sign" with a lower limit of -1 and a upper limit of 3 [x] dx
    2. Relevant equations
    I would like to know how to enter symbols for certain problems.

    I am lost when Apostol says "the notation [x] denotes the greatest integer <= x", i partially understand what he means.

    3. The attempt at a solution

  2. jcsd
  3. Aug 7, 2010 #2
    the notation [x] denotes the greatest integer <= x; means exactly what is said.
    [x] denotes the greatest integer less than or equal to x.
    [2.1] = 2 [2.9] =2

    Because 2 is the largest integer less than 2.1 and 2.9.

    The function when plotted looks like a staircase. You can compute the integral simply by adding the areas underneath the step; accounting for negative and positive area, ofcourse.

    The integral should be something like 2 if I am not mistaken.
  4. Aug 7, 2010 #3


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    Gold Member

    Let me give you a concrete example to illustrate [x]

    [3.4] means the greatest integer that is less than or equal to 3.4 which is 3

    The equal to is used when x is an integer itself, so

    [3] = 3
  5. Aug 7, 2010 #4
    thanks for the explanation guys
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