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#1 2012-07-21 15:46:41

Fruityloop
Member
Registered: 2009-05-18
Posts: 120

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.


The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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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!  smile


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
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Evaluate this integral

Hi Fruityloop;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#4 2012-07-23 00:09:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#5 2012-07-23 06:10:40

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#6 2012-07-23 06:27:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#7 2012-07-23 06:30:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Evaluate this integral

That is okay.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#8 2012-07-23 06:39:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#9 2012-07-23 06:40:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: Evaluate this integral

The wrong answer!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#10 2012-07-23 06:41:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#11 2012-07-23 06:44:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#12 2012-07-23 06:48:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#13 2012-07-23 06:51:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#14 2012-07-23 07:02:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#15 2012-07-23 07:04:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#16 2012-07-23 07:13:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#17 2012-07-23 07:18:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#18 2012-07-23 07:28:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#19 2012-07-23 07:34:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#20 2012-07-23 07:38:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#21 2012-07-23 07:46:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#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?

smile


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: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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#24 2012-07-23 09:55:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#25 2012-07-23 10:05:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

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

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