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#1 2012-06-03 22:36:53

amberzak
Member
Registered: 2012-03-16
Posts: 80

Harder Substitution

By using the Substitution u=cot theta or otherwise, find the integral of cot ^4 theta d theta


My teacher says there is a really simple way to do this, so it shouldn't take hours.

He also gave us a hint of writing down sec^3 theta and tan theta, but I can't see how we can get to that.


Any ideas?


Don't think outside the box. Think there is no box

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#2 2012-06-04 05:01:36

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Harder Substitution

Hi amberzak

Have you tried the substitution t=tan(theta)?


“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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#3 2012-06-04 05:06:47

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Harder Substitution

hi amberzak,


Bob

ps. I don't get the hint.  Threw it away and did without.


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#4 2012-06-04 05:17:35

amberzak
Member
Registered: 2012-03-16
Posts: 80

Re: Harder Substitution

Anon, I have not yet. How would I do that?
Bob, I am guessing it's still answer in process. I get so far and then couldn't get further. I think the sec^3 theta tan theta is a hint.


Don't think outside the box. Think there is no box

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#5 2012-06-04 05:22:15

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Harder Substitution

hi amberzak,

I couldn't make any sense of the hint.  My post above is complete.  I've just got to check by differentiation.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#6 2012-06-04 05:24:32

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Harder Substitution

Yes,  that works!  smile:):)

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#7 2012-06-04 05:30:02

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Harder Substitution

Hi Bob

Bob wrote:

Yes,  that works! 

Bob

I still can't understand the hint.


“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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#8 2012-06-04 05:43:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Harder Substitution


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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#9 2012-06-04 05:49:14

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Harder Substitution

Her voice is so thin compared to Chris Martin's.I cannot listen to Viva la Vida while listening to her.


“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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#10 2012-06-04 05:52:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Harder Substitution

Maybe, but Amber may like to see it.


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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#11 2012-06-04 05:54:35

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Harder Substitution

Who is Amber and what does she want to see?

EDIT:Oh,you meant amberzak! You never call people on this forum by their real names,even if you know them (with the sole exception of Bob).

Last edited by anonimnystefy (2012-06-04 05:55:36)


“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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#12 2012-06-04 06:25:29

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Harder Substitution

hi Stefy,

I still can't understand the hint.

Me neither.

Is it compulsory to follow a hint?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#13 2012-06-04 06:26:34

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Harder Substitution

bob bundy wrote:

Yes,  that works!  smile:):)

Bob

What was this then?


“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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#14 2012-06-04 07:01:04

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Harder Substitution

That was me being triumphant, because I had tested my integration and it works (ie. when you differentiate it,  you get cot^4 theta.)

Please look at post #3

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#15 2012-06-04 07:04:22

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Harder Substitution

Yes,I have seen your method. Why did you think it would work? And don't you think I would have immediately told you if there was something wrong with your working? smile

I have sent you an e-mail.


“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.

Offline

#16 2012-06-04 07:32:21

amberzak
Member
Registered: 2012-03-16
Posts: 80

Re: Harder Substitution

It's okay, my real name isn't amberzak.

What was the method you used bob? And thanks, you have been very helpful

The link you gave me doesn't work sad

Last edited by amberzak (2012-06-04 07:35:58)


Don't think outside the box. Think there is no box

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#17 2012-06-04 07:40:33

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Harder Substitution

See post #3

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#18 2012-06-04 08:55:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Harder Substitution

Hi amberzak;

The link you gave me doesn't work

Did you mean my link? It is working fine here.


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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#19 2012-06-08 23:14:06

amberzak
Member
Registered: 2012-03-16
Posts: 80

Re: Harder Substitution

It's working today big_smile


Don't think outside the box. Think there is no box

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#20 2012-06-08 23:29:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Harder Substitution

Hi amberzak;

Very good! The video is Bob's method so you can use it to strengthen your understanding of what he did.


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.

Offline

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