Solve Improper Integral: 2/(v^2-v) Without Calculator

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Discussion Overview

The discussion revolves around evaluating the improper integral of the function 2/(v^2-v) from 2 to infinity. Participants are exploring methods to solve this integral without the use of a calculator, focusing on techniques such as partial fractions and limits.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in solving the integral and requests assistance.
  • Another participant suggests setting up the integral as a limit and indicates that partial fractions might be necessary.
  • A third participant provides a specific formulation of the integral and proposes using partial fractions to simplify it, mentioning the potential for logarithmic results.
  • A later post shifts the topic to a historical question about the invention of integral calculus, leading to a brief debate about the contributions of Leibniz and Newton.

Areas of Agreement / Disagreement

There is no consensus on the solution to the integral, as participants are still discussing methods and expressing differing views on the historical context of integral calculus.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in evaluating the integral, and there are indications of uncertainty regarding the convergence or divergence of the integral.

Commodore
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I have tried to work this problem, but I keep getting the wrong answer. Please help...

Evaluate the integral from 2 to infinity of 2/(v^2-v). I cannot use a calculator and the answers that I get are nonsensical. PLEASE HELP!
 
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could you show your work?

i seems like you need to first setup the integral into the limit, and then the do the integral. It seems like a partial fractions. and then do the limits (easiest one first maybe it diverges? xD).
 
[tex]\int_2^{\infty}\frac{2}{v(v-1)}dv[/tex]

Looks pretty straight forward. Do you know how to do partial fractions?

Write

[tex]\frac{1}{v(v-1)} = \frac{A}{v}+\frac{B}{v-1}[/tex]

Solve for A and B. Rewrite the integral and you should get log or something. I think.
 
Last edited:
Thank you very, very much!
 
Does anyone know who invented the integral calculus?
 
It was Leibniz, Newton was a fraud!
 
Very useful comments there Kepler.
 

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