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#26 2010-09-28 08:12:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

Hi 123ronnie321;

Welcome to the forum! That is not the correct 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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#27 2010-12-10 07:09:58

Raven66
Member
Registered: 2010-12-10
Posts: 1

Re: Integration by Substitution

Some similar solved examples on integration by substitution are available at http://www.math24.net/change-of-variable.html.

Last edited by Raven66 (2010-12-10 07:10:39)

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#28 2010-12-10 13:40:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

Hi Raven66;

Welcome to the forum! That is a nice site. Some nice stuff on surface integrals there.


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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#29 2011-04-20 22:04:39

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Re: Integration by Substitution

Second try-

bobbym wrote:

Hi;

Here is an interesting integral done by substitution.

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#30 2011-04-20 22:30:31

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

Re: Integration by Substitution

Hi 123ronnie321,

Yes, how did you solve it?


"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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#31 2011-04-20 22:30:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

Hi 123ronnie321

Sorry, gAr, we were posting at the same time.


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.

Online

#32 2011-04-20 22:45:38

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

Re: Integration by Substitution

Hi bobbym,

Strange! Sage too couldn't do it.
Looks like the packages do not use the properties of definite integrals.


"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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#33 2011-04-20 22:56:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

You know when I posed this was a long time ago. That is exactly what I did too. No one got it for a long time. Very good work!


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.

Online

#34 2011-04-20 23:11:18

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

Re: Integration by Substitution

Yes, really a long time ago!
Thanks.

A similar kind of problem:


"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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#35 2011-04-20 23:18:02

123ronnie321
Member
Registered: 2010-09-28
Posts: 128

Re: Integration by Substitution

Hi bobbym,
Thank you. Nice problem.

Hi gar, Yes that is how i did it too!

Last edited by 123ronnie321 (2011-04-20 23:34:41)

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#36 2011-04-20 23:26:14

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

Re: Integration by Substitution

Hi 123ronnie321,

Okay, good one!


"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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#37 2011-06-30 23:23:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

hi everyone

could anyone tell me if this i correct,I'm trying to practice calculating integrals:

Last edited by anonimnystefy (2011-07-01 01:02:09)


“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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#38 2011-06-30 23:27:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

hi

here's the fifth problem cuz it couldn't fit into my last one:

Last edited by anonimnystefy (2011-06-30 23:40:13)


“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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#39 2011-06-30 23:40:03

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

hi

seventh problem:


“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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#40 2011-06-30 23:44:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

hi

can anyone tell me how to 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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#41 2011-06-30 23:50:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

Hi;

How do you integrate sin(u)?


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.

Online

#42 2011-07-01 01:02:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

hi bobbym

thanks for noticing.i corrected 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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#43 2011-07-01 01:06:25

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

Re: Integration by Substitution

Hi anonimnystefy,

All are right then.


CAS shows:

Wolframalpha suggests completing the square.

For some problems, you can use partial fractions.


"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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#44 2011-07-01 23:15:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

hi all

can anyone help me get:

Last edited by anonimnystefy (2012-06-22 07:29:59)


“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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#45 2011-07-02 00:14:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

anyone?


“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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#46 2011-07-02 00:15:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

Hi;

Have you done IBP?


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.

Online

#47 2011-07-02 00:21:31

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,518

Re: Integration by Substitution

no.

but i'm not sure how.


“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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#48 2011-07-02 00:32:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

Hi;

That looks like it will end up as an integration by parts.

First clean up the interior of the cosine.


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.

Online

#49 2011-07-02 00:35:48

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

Re: Integration by Substitution

Hi,

No need to use that!
It's only a constant angle there.
Using substitution would make it simpler.


"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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#50 2011-07-02 00:39:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Integration by Substitution

Hi;

the formula will give you

Which cleans up the constant 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.

Online

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