CALCULUS BUFFS come and help!

[GoldenGuppy]

What is the integral of 2/(x^2-x) from 2 to infinity?

Can you show me the process of doing it? Thanks a lot..

 

[N8Magic]

Oh jeez, if only I wasn't drunk, I could help you. Its an easy question mind you. (for those of use versed in the Calculus way).

Here's a bump anyways!

 

[Mday]

ignore the infinity, let it be from 2 to z

just integrate 2/(x^2-x) you'll want to do some partial fractions

then evaluate the resulting expression. from 2 to z. and take the limit as z approaches infinity

 

[N8Magic]

*sifting through the Calculus textbook right now*

 

[N8Magic]

*putting Calculus text away right now because this is way beyond me at this point*

If you still need help when I get up, I will do my best (if its not too late)

 

[Mday]

doing partial fractions

2/(xx-x) = A/(x-1) + B/x, solving for A and B

2/(xx-x) = 2 [ 1/(x-1) - 1/x ]

integrating: 2 [log(x-1) - log (x)] = 2log[(x-1)/x] {remember your logs, log is natural log, or ln if you want}

evaluation from "z" to 2, 2log[(z-1)/z] - 2log(1/2) = 2log[(z-1)/z] + log4 ... (remember your logs)

take the limit as z approaches infinity yields ... 2 log(1) + log4 = log 4

 

[PakG1]

Can't remember integration by parts right now but calculus is lovely stuff. Really! Love how it's used in almost every academic school of thought that requires [edit]numbers[/edit], bar computers.

edit: Looks like mday did it while I was typing.

 

[Mday]

you definitely do not want to do this by parts, you have to do it twice depending on how slick you are...

 

[PakG1]

Ya, whatever it was, my brain's kinda fuzzy rite now.

 

[xtreme2k]

Int by parts is actually very 'easy' for errors therefore usually not the perferred way to solve a problem. Anyway, how to use int by parts in problem? I seriously forgot all these integration stuff ...

 

[Mday]

you can separate it into 2/(x-1) and 1/x

 

[Mday]

isn't it interesting that this integration converges to a finite number =)

that's my favorite part of calculus... you get sums to infinity converging

and sums of little nothings being values other than 0...

 

[Mday]

i think i'll poke around here until i get a thank you...

 

[N8Magic]

Thank you.

 

[PakG1]

Calculus is paradoxical. A finite area from an infinite number of x and y-values. It's all very cool, anyway, especially Taylor series. Wonder what vector calculus is like.

 

[Mday]

vector calculus is boring, until you get to the end... those last 2 theorems are a whopper =)

 

[Mday]

e^ipi + 1 = 0 baby!!!