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#1 2012-07-22 13:46:41
- Fruityloop
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Evaluate this integral
This integral comes from trying to get the surface area of y=1/x rotated about the x-axis.
evaluate the integral
Good luck! It's a toughie.
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#2 2012-07-23 13:55:12
- noelevans
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Re: Evaluate this integral
Problems of this nature (integrals obtained by rotation as mentioned) if they are amenable to integral tables or substitution methods are usually highly rigged. Rotation problems like this with just any old function f(x) usually generate horrendous integrands not amenable to elementary methods.
This may be one of those "bad" ones. I tried several different substitutions (algebraic, trigonometric, integration by parts) and got nowhere.
Good luck with it! 
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
#3 2012-07-23 16:35:22
- bobbym
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Re: Evaluate this integral
Hi Fruityloop;
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#4 2012-07-23 22:09:44
- anonimnystefy
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Re: Evaluate this integral
Hi bobbym
Check your first step after the v-substitution.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#5 2012-07-24 04:10:40
- bobbym
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Re: Evaluate this integral
Hi;
I am not sure where you mean.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2012-07-24 04:27:19
- anonimnystefy
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Re: Evaluate this integral
Sorry, mybad. I forgot the substitution of differentials.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#7 2012-07-24 04:30:26
- bobbym
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Re: Evaluate this integral
That is okay.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#8 2012-07-24 04:39:26
- anonimnystefy
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Re: Evaluate this integral
What does M spit out for the integral?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#9 2012-07-24 04:40:16
- bobbym
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Re: Evaluate this integral
The wrong answer!
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#10 2012-07-24 04:41:39
- anonimnystefy
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Re: Evaluate this integral
Can you post it? I am interested to see what it is because you suggested using it.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#11 2012-07-24 04:44:49
- bobbym
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Re: Evaluate this integral
I hesitate to put his ugly solution that is magic next to mine.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#12 2012-07-24 04:48:02
- anonimnystefy
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Re: Evaluate this integral
Hi bobbym
Wouldn't the first term simplify to 1/2 *arcsinh(x**2) ?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#13 2012-07-24 04:51:44
- bobbym
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Re: Evaluate this integral
Hi;
M's answer? I do not know. I only know that it comes out of nowhere. When I follow his steps I do not get that. Also the answer I get is wrong. That is why I did it my way. It is longer but at least I think it is correct.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#14 2012-07-24 05:02:59
- anonimnystefy
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Re: Evaluate this integral
Do the integral in Wolfram and click show steps. Interesting behaviour.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#15 2012-07-24 05:04:55
- bobbym
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Re: Evaluate this integral
Yes, that is what he gets. When I follow along the answer is different. Also it has a complex fungus attached to it!
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#16 2012-07-24 05:13:20
- anonimnystefy
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Re: Evaluate this integral
Yes, the answer is different from what he gets in the "Show steps" solution! But I do not see any complex stuff.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#17 2012-07-24 05:18:05
- bobbym
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Re: Evaluate this integral
Did you work towards the solution using M? You will get the wrong answer.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#18 2012-07-24 05:28:34
- anonimnystefy
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Re: Evaluate this integral
Wolfram spits out the wrong answer.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#19 2012-07-24 05:34:00
- bobbym
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Re: Evaluate this integral
Is that a question? The package and Alpha are not the same thing. He gets the wrong answer on the integral because of the partial fraction decomposition. When I plug in x =1. he spit out a complex number!
Maple on the other hand in this case does the integration correctly.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#20 2012-07-24 05:38:56
- anonimnystefy
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Re: Evaluate this integral
But I don't have M.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#21 2012-07-24 05:46:52
- bobbym
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Re: Evaluate this integral
Well, then why did you want to see what it did?
I only mentioned the packages here for completeness. The whole thing can be done by hand.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#22 2012-07-24 07:07:29
- noelevans
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Re: Evaluate this integral
hi bobbym,
In going from the second step of your answer in post #3 to the third step did you miscopy the x^5 as an x^4? Should dx = ((-1/4)x^5)du?
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
#23 2012-07-24 07:25:46
- anonimnystefy
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Re: Evaluate this integral
Probably is.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#24 2012-07-24 07:55:43
- bobbym
- Administrator
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Re: Evaluate this integral
Hi noelevans;
Yes it is. I am fixing the above. Thanks.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#25 2012-07-24 08:05:07
- anonimnystefy
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Re: Evaluate this integral
Minor error compared to M's. Speaking of it, are you going to feedback them to llet them know about it?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón