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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

Part one. Introduction.

**"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"**

** Thomas Ioannes Stiltes.** ...

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

hi 21122012

Thank you. That is very clear. I look forward to part two.

Nice avatar.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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

The integral at the bottom is incorrect. It needs the integration constant C.

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

Watch longer, Stefy. He puts in definite limits.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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

Hi Bob

I was on my phone when I looked at that picture and it didn't show it as an animation. 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

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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

Hi bob.

I prepare the following animations. This quite labor-consuming production.

**"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"**

** Thomas Ioannes Stiltes.** ...

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

hi

I can believe it is ... but if you want people to understand what you are talking about ...

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

I want to notice that the left drawing has bottom and top limits is two values:

because:

bob bundy wrote:

hi

I can believe it is ... but if you want people to understand what you are talking about ...

Bob

While let only look. It has to be postponed in subconsciousness then to associate with the told

*Last edited by 21122012 (2013-01-05 07:23:19)*

**"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"**

** Thomas Ioannes Stiltes.** ...

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

f'(0)x=0

What is f ?

Bob

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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

bob bundy wrote:

f'(0)x=0

What is f ?

Bob

I there added. That absolutely correctly there had to be two blue points and any red.

*Last edited by 21122012 (2013-01-05 07:53:17)*

** Thomas Ioannes Stiltes.** ...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Please use the edit button to add to posts. Multiple posts to yourself are difficult to follow.

**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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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

If a formula:

to represent in the form of segment of the line:

which will be expressed by a formula:

that the bottom limit - value of argument:

of the function , the top limit - value of argument: of the function .The first point of a segment of line - value of a derivative:

, the last point of a segment of line - value of a derivative: .The line on which located the segment of line has a formula:

.If all line - f (t):

And if the line consists more than of one part:

or

P.S.

*Last edited by 21122012 (2013-01-05 12:58:51)*

** Thomas Ioannes Stiltes.** ...

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

Then, what is the integral of f(x)=x?

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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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

anonimnystefy wrote:

Then, what is the integral of f(x)=x?

This phrase has in itself no concept of integral. Write a formula.

May be this down line?

*Last edited by 21122012 (2013-01-05 13:03:24)*

** Thomas Ioannes Stiltes.** ...

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

I think you know well what I mean..

What is the integral of the function f(x)=x with respect to x?

Here lies the reader who will never open this book. He is forever dead.

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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

anonimnystefy wrote:

I think you know well what I mean..

What is the integral of the function f(x)=x with respect to x?

*Last edited by 21122012 (2013-01-05 13:15:06)*

** Thomas Ioannes Stiltes.** ...

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

The first one.

Here lies the reader who will never open this book. He is forever dead.

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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

anonimnystefy wrote:

The first one.

What exactly do you want to learn about this integral? It is a half of the area of a square.

The derivative of this area will be the party of this square.

*Last edited by 21122012 (2013-01-05 13:19:08)*

** Thomas Ioannes Stiltes.** ...

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

Well I think it will be x^2/2+1000.

Here lies the reader who will never open this book. He is forever dead.

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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

anonimnystefy wrote:

Well I think it will be x^2/2+1000.

For example so?

I won't understand sense of a question. Here to you in a general view a formula:

*Last edited by 21122012 (2013-01-05 13:41:35)*

** Thomas Ioannes Stiltes.** ...

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

hi 21122012,

Please forgive me for the long gap in my posts.

I need to review what has been said.

in post #8 you wrote:

I think this means:

If this is correct, then I understand post #8.

Now I review post #12.

in post #12 you wrote:

I call this "integration by change of variable":

I understand this.

Then

you wrote:

Did you mean ?

I think you are saying:

"Use a partial sign when the integral is indefinite" Is this correct ?

I regret that I do not understand the diagram in post #14 .

Bob

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**21122012****Member**- Registered: 2012-11-16
- Posts: 278

Hi Bob

bob bundy wrote:

hi 21122012,

Please forgive me for the long gap in my posts.

I need to review what has been said.

in post #8 you wrote:I think this means:

If this is correct, then I understand post #8.

...

I regret that I do not understand the diagram in post #14 .

Bob

Sense of written in post#8 - is represented on the chart in post #14 !!!

In rectangular system of coordinates the segment of line:

image as a function increment:

in the form of the sum:

of identical points is used:

The distance between the next points will be equal:

In the Cartesian system of coordinates the distance between the next points equal is used

then points from which the segment of line consists are:

Points of a piece are inadequate and matter equal to value of derivatives at argument change.

Bob, look this animation. When on the right the green segment of line

increases in a size at one a point up at the same time on the right its equivalent the area of a circle increases by one circumference and so up to the end: more and more points in a segment of line - more and more circumferences in a circle. Circumferences of the various size - a points of various value. In the beginning the circumference is equal to zero - the point is equal to zero. At the end the circle is equal to a maximum - a point same.bob bundy wrote:

...

Thenyou wrote:Did you mean ?

Bob

Part second. Geometrical and graphic interpretation of concept a derivative on the example of function

If it is badly visible it is possible to look here.

*Last edited by 21122012 (2013-01-06 18:15:35)*

** Thomas Ioannes Stiltes.** ...

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

hi 21122012

I need time to understand this. I will post again later.

bobbym: When I check up on a thread, I start with the first post after my last post and work forward. So "double posts" are not a problem for me. If another poster edits a post I have already looked at, I may well miss the edit.

Bob

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

Hi 21122012

I have a problem with

I have made a spreadsheet using Excel.

The first row shows values of 'r' from 0 to 1 in steps of 0.1

The second row shows values of f(r) = pi r^2

The third row uses the trapezium rule to calculate (approximately) the area of each section.

The fourth row adds these up to give the area under the graph of f(r)

Using the final value as a correct volume of a cone I calculated the height of the cone.

The fifth row shows the height for each r value.

The final row shows the volume, calculated using the correct formula.

As expected this value agrees with your area under graph calculation for the final column (P). This should happen because I used the coluimn P values to compute 'h'.

But it does not show that your area under graph figures are correct.

So the integration at the start of this post does not give correct volumes.

Why do you think this is ?

Bob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi Bob;

I know you are checking the posts but I do not want to turn yet another of his threads into a soliloquy. 10 -12 posts to himself is not a thread, A double post is sometimes necessary and ordinarily I do not care. Two threads closed and 3 more deleted due to rule infractions is too much.

I have overlooked the monkeys, idiots, fools and vain moderator cracks. I have overlooked the soliciting for money. I have overlooked him whimsically starting new threads as a means to continue the same infraction that he was warned about in the old ones. Then he asks me to close the threads. I have had complaints as you know.

I would like the thread to stay open, that means conversation, not him posting more of the same to himself. I intend to make sure that this thread stays on track.

I may well miss the edit.

You do not have to worry about that. It will be posted again 26 more times over 3 threads.

**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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