Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#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)

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#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.

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

#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)

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#38 2011-06-30 23:27:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#39 2011-06-30 23:40:03

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#40 2011-06-30 23:44:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#41 2011-06-30 23:50:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

Re: Integration by Substitution

Hi;

How do you integrate sin(u)?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#43 2011-07-01 01:06:25

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#45 2011-07-02 00:14:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#46 2011-07-02 00:15:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

Re: Integration by Substitution

Hi;

Have you done IBP?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,819

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

Offline

#48 2011-07-02 00:32:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,506

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

Board footer

Powered by FluxBB