Evaluating Integral: \int\frac{4}{x^2-1}

  • Thread starter Thread starter danielatha4
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary

Homework Help Overview

The discussion revolves around evaluating the integral \(\int\frac{4}{x^2-1}\), which falls under the subject area of calculus, specifically integral calculus.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to simplify the integrand using partial fraction decomposition and evaluates the integral, but expresses uncertainty about the correctness of their result.

Discussion Status

Some participants engage in verifying the calculations and suggest that a possible error could stem from rounding or calculator input. There is an acknowledgment of a potential mistake, but no consensus on the exact nature of the error has been reached.

Contextual Notes

The original poster mentions evaluating the integral from 2 to 3, indicating specific bounds for the definite integral, but does not provide additional context on any constraints or rules imposed by the homework assignment.

danielatha4
Messages
113
Reaction score
0

Homework Statement


[tex]\int[/tex][tex]\frac{4}{x^2-1}[/tex]



Homework Equations





The Attempt at a Solution


I thought I had this right...

[tex]\frac{4}{x^2-1}[/tex] = 2 ([tex]\frac{1}{x-1}[/tex]-[tex]\frac{1}{x+1}[/tex])

therefore,

[tex]\int[/tex][tex]\frac{4}{x^2-1}[/tex]=2(ln(x-1)-ln(x+1))

I then have to evaluate from 2 to 3 and I get .814, but it isn't right.
 
Last edited:
Physics news on Phys.org
Nevermind, I believe I figured it out.

Edit: Okay, I don't understand where I went wrong. Any help please?
 
Last edited:
I get log(9/4) ≈ 0.81093
Perhaps you entered it wrong in a calculator?
 
Oh gees... rounding error... thanks
 

Similar threads

  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K
Replies
3
Views
2K
Replies
7
Views
2K
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 22 ·
Replies
22
Views
3K
Replies
20
Views
2K