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

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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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

Hi Fruityloop;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Hi bobbym

Check your first step after the v-substitution.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

Hi;

I am not sure where you mean.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

That is okay.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

The wrong answer!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

I hesitate to put his ugly solution that is magic next to mine.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

Yes, that is what he gets. When I follow along the answer is different. Also it has a complex fungus attached to it!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

Did you work towards the solution using M? You will get the wrong answer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Wolfram spits out the wrong answer.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

But I don't have M.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Probably is.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,240

Hi noelevans;

Yes it is. I am fixing the above. Thanks.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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.

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