Computing the value of an integral from Apostol I

[Press90]

Homework Statement

The notation [x] denotes the greatest integer <= x


"integral sign" with a lower limit of -1 and a upper limit of 3 [x] dx

Homework 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.

The Attempt at a Solution

n/a

 

[╔(σ_σ)╝]

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.

 

[thrill3rnit3]

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

 

[Press90]

thanks for the explanation guys