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#1 2012-07-21 15:46:41
- Fruityloop
- Member
- Registered: 2009-05-18
- Posts: 143
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 2012-07-22 15:55:12
- noelevans
- Member
- Registered: 2012-07-20
- Posts: 236
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.
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#3 2012-07-22 18:35:22
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Evaluate this integral
Hi Fruityloop;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#4 2012-07-23 00:09:44
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
Hi bobbym
Check your first step after the v-substitution.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#5 2012-07-23 06:10:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2012-07-23 06:27:19
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
Sorry, mybad. I forgot the substitution of differentials.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#7 2012-07-23 06:30:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Evaluate this integral
That is okay.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2012-07-23 06:39:26
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
What does M spit out for the integral?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#9 2012-07-23 06:40:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Evaluate this integral
The wrong answer!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2012-07-23 06:41:39
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
Can you post it? I am interested to see what it is because you suggested using it.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#11 2012-07-23 06:44:49
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2012-07-23 06:48:02
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
Hi bobbym
Wouldn't the first term simplify to 1/2 *arcsinh(x**2) ?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#13 2012-07-23 06:51:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2012-07-23 07:02:59
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
Do the integral in Wolfram and click show steps. Interesting behaviour.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#15 2012-07-23 07:04:55
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2012-07-23 07:13:20
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#17 2012-07-23 07:18:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2012-07-23 07:28:34
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
Wolfram spits out the wrong answer.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#19 2012-07-23 07:34:00
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#20 2012-07-23 07:38:56
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
But I don't have M.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#21 2012-07-23 07:46:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#22 2012-07-23 09:07:29
- noelevans
- Member
- Registered: 2012-07-20
- Posts: 236
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.
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#23 2012-07-23 09:25:46
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Evaluate this integral
Probably is.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#24 2012-07-23 09:55:43
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#25 2012-07-23 10:05:07
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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