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#26 2015-07-26 08:32:28

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

Re: Definite Integrals of Inverse Functions

Why do you think so?


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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#27 2015-07-26 08:34:17

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

Re: Definite Integrals of Inverse Functions

Is that the graph of f or f^-1?


“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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#28 2015-07-26 08:35:00

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

Re: Definite Integrals of Inverse Functions

That is the graph of f(x).


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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#29 2015-07-26 08:37:31

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

Re: Definite Integrals of Inverse Functions

Then, the coordinates of C should be (f^-1(pi/2), pi/2).


“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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#30 2015-07-26 08:40:17

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

Re: Definite Integrals of Inverse Functions

Hi;

Algebraically, I can not even find the inverse function of his function.

You do not need it. C is still (pi/2,f(pi/2)). Now just get the area on the left of f(x).


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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#31 2015-07-26 08:42:32

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

Re: Definite Integrals of Inverse Functions

That is not correct. That would not get the wanted integral. It would give:

Last edited by anonimnystefy (2015-07-26 08:42:51)


“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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#32 2015-07-26 08:46:28

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

Re: Definite Integrals of Inverse Functions

Hmmm, what do you get?


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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#33 2015-07-26 08:48:24

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

Re: Definite Integrals of Inverse Functions

I cannot get it completely simplified yet. (without f^-1, that is).

Last edited by anonimnystefy (2015-07-26 08:48:41)


“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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#34 2015-07-26 08:49:13

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

Re: Definite Integrals of Inverse Functions

Did you see post #12?

I am just following through on zetafunc's idea, maybe I misunderstood what he was saying?!

Glad to see you back in the forum.


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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#35 2015-07-26 08:58:17

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

Re: Definite Integrals of Inverse Functions

Yes, I am going by that idea as well.

Thank you! Nice to see you again!


“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

#36 2015-07-26 09:17:04

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

Re: Definite Integrals of Inverse Functions

Yes, I am going by that idea as well.

I have tried your idea and it leads to the same answer. Both methods are valid!


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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#37 2015-07-26 21:07:04

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Definite Integrals of Inverse Functions

anonimnystefy wrote:

Hi bobbym

The y-coordinate of C needs to be pi/2, though, not the x coordinate.

That is what I mean, exactly.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#38 2015-07-26 21:07:28

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

Re: Definite Integrals of Inverse Functions

I think the answer is the same.


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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#39 2015-07-27 00:49:37

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Definite Integrals of Inverse Functions

I have the same idea but why?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#40 2015-07-27 07:00:59

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

Re: Definite Integrals of Inverse Functions

I have solved both methods.


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

#41 2015-07-27 12:03:00

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Definite Integrals of Inverse Functions

But you are not telling me how to.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#42 2015-07-27 12:07:13

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

Re: Definite Integrals of Inverse Functions

Did you understand the first one?

For the second method I used this page:

http://www.purplemath.com/modules/invrsfcn.htm


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

#43 2015-07-30 11:54:45

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Definite Integrals of Inverse Functions

I already knew whatever is in the page, but how does that help me integrate?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#44 2015-07-30 11:56:44

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

Re: Definite Integrals of Inverse Functions

For the second method I used EM to get an approximate 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.

Offline

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