Register to reply

Computing the value of an integral from Apostol I

by Press90
Tags: apostol, calculus, integral, theorem
Share this thread:
Press90
#1
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

n/a
Phys.Org News Partner Science news on Phys.org
Sapphire talk enlivens guesswork over iPhone 6
Geneticists offer clues to better rice, tomato crops
UConn makes 3-D copies of antique instrument parts
╔(σ_σ)╝
#2
Aug7-10, 10:18 PM
╔(σ_σ)╝'s Avatar
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.
thrill3rnit3
#3
Aug7-10, 10:18 PM
PF Gold
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

Press90
#4
Aug7-10, 10:57 PM
P: 3
Computing the value of an integral from Apostol I

thanks for the explanation guys


Register to reply

Related Discussions
Computing an improper integral Calculus & Beyond Homework 2
Computing a double integral with given vertices Calculus & Beyond Homework 1
[Numerical] Computing a contour of an integral function Calculus 0
Computing triple integral Calculus & Beyond Homework 7
Optical Computing: special issue - Natural Computing, Springer General Physics 0