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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
Member
Registered: 2013-03-09
Posts: 874
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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,700

### Re: A nice integral

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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
The knowledge of some things as a function of age is a delta function.

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## #7 2014-02-06 03:14:59

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,700

### Re: A nice integral

Hi;

Did you test that second answer?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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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
Registered: 2013-03-09
Posts: 874
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
Member
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: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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
The knowledge of some things as a function of age is a delta function.

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## #13 2014-02-08 09:07:04

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,700

### 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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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
The knowledge of some things as a function of age is a delta function.

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## #15 2014-02-08 09:50:32

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,700

### Re: A nice integral

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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
The knowledge of some things as a function of age is a delta function.

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## #17 2014-02-08 10:00:57

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,700

### Re: A nice integral

That is okay, happens to me too.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Offline