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

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In summary, the individual is seeking help with evaluating the integral from 2 to infinity of 2/(v^2-v) without using a calculator. They mention getting nonsensical answers and ask for assistance. Another person suggests setting up the integral as a limit and using partial fractions. They also mention the inventor of integral calculus being Leibniz and calling Newton a fraud.
  • #1
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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  • #2
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).
 
  • #3
[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.
 
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  • #4
Thank you very, very much!
 
  • #5
Does anyone know who invented the integral calculus?
 
  • #6
It was Leibniz, Newton was a fraud!
 
  • #7
Very useful comments there Kepler.
 

1. What is an improper integral?

An improper integral is an integral where either the upper or lower limit of integration is infinite, or the integrand function is undefined or discontinuous at some point within the interval of integration.

2. How do you solve an improper integral?

To solve an improper integral, you need to break it into smaller integrals, evaluate each integral, and then take the limit as the boundaries of integration approach infinity or the point of discontinuity.

3. Why can't we use a calculator to solve improper integrals?

Calculators are not able to handle infinite limits and discontinuous functions, which are often present in improper integrals. Therefore, it is not possible to solve them using a calculator.

4. What is the general approach to solving improper integrals?

The general approach to solving improper integrals is to first identify the type of improper integral (type 1 or type 2), then rewrite it as a limit of a proper integral, evaluate the integral, and finally take the limit as the boundaries approach infinity or the point of discontinuity.

5. How do you solve the specific improper integral 2/(v^2-v) without a calculator?

To solve this improper integral, you need to first factor out a v from the denominator to make it (v-1) and then use partial fractions to break the integral into two smaller integrals. Then, you can solve each integral separately and take the limit as v approaches infinity to get the final answer.

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