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Computing the value of an integral from Apostol I

by Press90
Tags: apostol, calculus, integral, theorem
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Aug7-10, 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

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Aug7-10, 10:18 PM
╔(σ_σ)╝'s Avatar
P: 849
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.
Aug7-10, 10:18 PM
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thrill3rnit3's Avatar
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

Aug7-10, 10:57 PM
P: 3
Computing the value of an integral from Apostol I

thanks for the explanation guys

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