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#1 2014-02-05 22:59:23

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

A nice integral

integral of 1/(x^4+x^2+1):D:D

Last edited by Yusuke00 (2014-02-05 23:00:34)

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#2 2014-02-06 00:35:56

Nehushtan
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From: London
Registered: 2013-03-09
Posts: 615
Website

Re: A nice integral

where w is the complex number
.


and you can integrate normally.

NB: Although w is complex, you can integrate as if you were doing normal real integration.


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#3 2014-02-06 00:58:16

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: A nice integral

ok i understand....thank you!

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#4 2014-02-06 01:11:38

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: A nice integral

integral of sqrt(x-x^2)

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#5 2014-02-06 01:44:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: A nice integral

Hi;


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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#6 2014-02-06 02:58:48

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

Re: A nice integral

Hi Yusuke00

The first can also be solved using x^4+x^2+1=(x^2-x+1)(x^2+x+1) without complex numbers.

For the second one, I am getting

Last edited by anonimnystefy (2014-02-06 03:00:07)


“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 2014-02-06 03:14:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: A nice integral

Hi;

Did you test that second answer?


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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#8 2014-02-06 20:53:51

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: A nice integral

f:[0,3]->R f(x)=max{3-x,2x+[x]} . Show that f is integrable on[0,3] and calculated integral of f(x)

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#9 2014-02-06 21:48:48

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: A nice integral

integral of 1/(sin^4x+cos^4x)dx

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#10 2014-02-07 00:42:02

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 615
Website

Re: A nice integral

Yusuke00 wrote:

f:[0,3]->R f(x)=max{3-x,2x+[x]} . Show that f is integrable on[0,3] and calculated integral of f(x)

f is integrable because it is piecewise continuous (except at the right-hand end point), i.e. it is continuous over the subintervals [0, 1), [1, 2), and [2, 3). (It doesn’t matter if it’s not continuous at an end point.)

Last edited by Nehushtan (2014-02-08 03:48:30)


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#11 2014-02-07 02:21:15

gAr
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Registered: 2011-01-09
Posts: 3,479

Re: A nice integral


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#12 2014-02-08 03:08:59

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

Re: A nice integral

bobbym wrote:

Hi;

Did you test that second answer?

Yeah.


“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 2014-02-08 09:07:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: A nice integral

Hi;

When you differentiate back, do you get the same function? I do not.


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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#14 2014-02-08 09:40:03

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

Re: A nice integral

I do. What do you get?


“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 2014-02-08 09:50:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: A nice integral


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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#16 2014-02-08 09:53:15

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

Re: A nice integral

Oh, sorry, I read it as 1/sqrt(...). That makes it different, sorry.


“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 2014-02-08 10:00:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: A nice integral

That is okay, happens to me too.


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.

Offline

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