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Computing the value of an integral from Apostol I 
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#1
Aug710, 09:05 PM

P: 3

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 n/a 


#2
Aug710, 10:18 PM

P: 850

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. 


#3
Aug710, 10:18 PM

PF Gold
P: 712

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 


#4
Aug710, 10:57 PM

P: 3

Computing the value of an integral from Apostol I
thanks for the explanation guys



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