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#1 2014-02-05 22:59:23
- Yusuke00
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- 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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#3 2014-02-06 00:58:16
- Yusuke00
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- Posts: 43
Re: A nice integral
ok i understand....thank you!
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#4 2014-02-06 01:11:38
- Yusuke00
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Re: A nice integral
integral of sqrt(x-x^2)
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#5 2014-02-06 01:44:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2014-02-06 02:58:48
- anonimnystefy
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- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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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
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- 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
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- Registered: 2013-03-09
- Posts: 957
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)
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 doesnt matter if its 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
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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: 16,049
Re: A nice integral
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2014-02-08 09:40:03
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2014-02-08 09:53:15
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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