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bob bundy wrote:

I am sorry to have to say this, because you have clearly put a lot of effort into your ideas. I have spent many hours trying to understand these, but I am no clearer than I was at the start.

Sorry.

Bob

Hi bob!

Here initial postulate of STRUCTURAL ANALYSIS:

I don't decide to translate it into English not to lose meaning.

Hi to All

The Fundamental Theorem of Calculus proves that:

1. That differentiation and antidifferentiation are essentially inverse processes:

2. How to evaluate a definite integral using the antiderivative of the integrand:

where F is an antiderivative of f (i.e., F' = f).

I think that on it the correct theory comes to an end.

Nobody proved it and it doesn't make sense.

Because:

bob bundy wrote:

But I will teach you to use the rules properly.

works for both.

Bob

You didn't explain to me as it is possible using to receive ONE formula TWO various answers one of which is 3 times more than another.

This is THREE volumes !!!

So in Structural Analysis.

Write as it looks at you:

bob bundy wrote:

21122012 wrote:You here understand everything?

No.

Bob

Hi bob

General view of these two expressions the identical:

You could teach me to that how to define the rule for integration. From where it is known that in one case one of variables for other variable is a constant and in other case they depend from each other. How to you it is prompted by a formula? Or each person establishes calculation rules itself voluntarily. After all answers turn out different.

anonimnystefy wrote:

Hi Bob

I think I finally understand what he means by schedule- graph!

Yes but it not I am the robot so translates.

Here so it translated your phrase:

On English: "I think I finally understand what he means by schedule- grap"

->

On Russian: "Я думаю, что наконец понимаю то, что он подразумевает графиком - граф!"

Hi bob!

You here understand everything?

from left to right:

1. The segment of line.

2. The rectangular system of coordinates (for drawing of charts and schedules of independent sizes).

3. Cartesian coordinate system (for schedules of dependent sizes)

4.Cartesian coordinate system

bob bundy wrote:

...

...

Similarly, the total derivative with respect to h is:

...

Bob

Wikipedia:

Identical type of expressions - decide differently. On the ode of a variable the derivative undertakes, other letter registers.

bob bundy wrote:

2122012 wrote:.I do not understand you.

total derivative. What do you want me to differentiate with respect to?

Two functions, each function of two variables, in one option dependent are given, in the other - of the independent - is unclear on what function to consider a total derivative...

This is cardsharpering instead of exact science.

bob bundy wrote:

hi 21122012,

Oh thank you. I am so pleased you have decided to ask me to explain integration.

To work out a volume you divide the solid into thin slices, each one dh in thickness and add them up

For a cylinder each slice is a circle with a radius of r.

Now add them up

Now, and this is the important bit, for a cylinder, every slice is the

same size, so the pi r^2 term isconstantas h varies.

Everything is up to this point all is correct

bob bundy wrote:

If V = 0 when h = 0 then C = 0

I don't understand this thought!

bob bundy wrote:

For a cone each slice is again a circle with a radius of r.

But the circles are not all the same size. As h increases from o to H, the radius changes from 0 to R.

So \pi r^2 is

not constant.

Gallantly!

bob bundy wrote:

STOP!!!

Here mistake!!! I constantly speak to you about it, but you don't hear me!!!

It not algebra! At the left you have two independent variables therefore the result will be one. On the right two dependent variables therefore the result will be another. These two expressions aren't EQUAL! Use WolframAlfa, it will yield to you two various results!

Look this. You equate two red areas to which shooters point. These areas aren't equal.

bob bundy wrote:

So the result is different.

Do you understand now how integration works ?

Add up the slices but take account of whether they are all the same size, or change as h changes.

Bob

Bob you don't make laugh me. I and WolframAlpha we know as integration works.

P.S.

bob bundy wrote:

hi 21122012,

...

...

Bob

BECAUSE:

bob bundy wrote:

Do you understand now how integration works ?

Bob

P.P.S.

Bob!

It already amused me. Let's talk about the serious. Here one from the most important keys to Structural Analysis. You here understand everything?

from left to right:

1. The segment of line.

2. The rectangular system of coordinates (for drawing of charts and schedules of independent sizes).

3. Cartesian coordinate system (for schedules of dependent sizes)

4.Cartesian coordinate system

Hi Bob!

You recognize an error of calculus which calls cylinder volume as volume a cone or give me a formula of uncertain integral for cylinder volume. But there can be at you such science which can't give a formula of volume of the cylinder? Then your science is necessary to nobody!

Hi bob.

Write please a formula: [math ]V_ {cylinder} = \int... continue further [/math]. I want to look at it!!!

.

21122012 wrote:

bob bundy wrote:

You didn't prove to me that a formula

Bob

21122012 wrote:

It is a special case of a general view:

bob bundy wrote:

hi 21122012

Here you say

How can this be from o to r ? The variable is h.

Bob

P.S.

Is analog:

Hy bob

You forgot about what we speak. More true you forgot that moment because of which our dialogue began. Therefore you displaced sense in other party. I will remind you and you will see that you lost the conversation reason.

"....I will show one real mistake. But usually after such my subjects in Russia deleted at once. I will try here. We look the link:

http://en.wikipedia.org/wiki/Partial_derivative

We see a formula of a full derivative of volume of a cone on height:

We integrate this derivative and we receive... cylinder volume:

...."You remembered why we started talking about a cone and the cylinder? Therefore when we tell about volumes of these two geometrical figures that I always I speak about them and I remember the reason for which we speak about it. And you tell everything that doesn't treat at all a subject of our dispute. You didn't prove to me that a formula

it is cone volume. And still didn't give integral for calculation of volume of the cylinder which would differ from this formula THOUGH SOMETHING!

anonimnystefy wrote:

bob bundy wrote:That is not correct. You cannot have h both in the integration limits and as the variable which you are integrating with respect to...

This isn't an error. It is an unnecessary duplicator of a variable of a mntegrirovaniye. In the main theorem of calculation it is a case when the variable doesn't lie in an interval and is the interval end.

bob bundy wrote:

hi 21122012

Here you say

How can this be from o to r ? The variable is h.

Hi bob!

WOW!!!!!!!!

Look this:

It is a special case of a general view:

bob bundy wrote:

Note:

It is a special case. You choose only one option from all possible options of height. Such, when height равнв to basis radius. I didn't think that it is difficult for understanding.

bob bundy wrote:

And you say

I couldn't say such nonsense. It not cone volume, because it cylinder volume.

bob bundy wrote:

Note:

This is my last word on integration.

Bob

You don't understand difference of a variable from value of a variable which is constants.

If you took two independent

variables, then made their dependent

Then took values of these dependent variables

these values can't become independent variables

It is absurdity!

Function of a type:

in a geometrical form of a mnterpretation where - x radius, y - height can be constructed only in the form of cylinder volume.

The volume of cone can be constructed only if

Excuse don't take offense at me but with such representation of integration as at you it is impossible to accuse me of mistakes. It is frivolous. If you saw it as someone somewhere goes figures in chess you will speak to the grand master that you will win against him in advance. Once again I am sorry but you told the first that I am mistaken. I am not mistaken. I can teach as to do correctly those who is mistaken.

I translate from English. I can't understand that you want. What mine have to be actions?

Bob!

You don't understand that such differential. It not SMALL INCREMENT. This ELEMENTARY INCREMENT! And you use the SMALL INCREMENT.

You didn't read post #28. Read, I there show a difference. But I now will repeat in relation to your example. You have the circle area. Not important what radius. Understand, radius length yet has no value! This area of a circle - the area, but not volume! This is element of Planimetrics, but not element of Solid Geometry. You understend me? This element of Planimetrics has its radius?

Now take the radius one point smaller or one point more and construct the circle area. Put from above on the first circle. Look at thickness sideways. It will be elementary volume of

. If you put just the same circle, the circle area increased by distance to other circle not including other circle is will be elementary volume of . Because Though eventually will reach only size Because

Now most important!

When you build cone volume with height equal to basis (!) radius that at distance from a beginning point (from top) at any distance on height with you will be placed the circle with the same radius (!) is a key to understanding of integration! In any point of height there will be element of Planimetrics in the form of a circle of the same radius. If height isn't equal to radius, and is its function, at each distance from top there will be a circle CORRESPONDING to value of function!

Therefore no trapezes will exist! Trapezes are delusions (errors) of Calculus.

They have no place to undertake. They won't appear anywhere because there will be no two distances from top on which there will be identical circles!

There will be only elementary truncated cones.

In what difference between

and

Which in the first case creates volume a cone, and in the second case creates cylinder volume???!!!

Everything is concluded in a difference of these two expressions:

prompts that at distance from top circle will settle down. prompts that at any distance from top IDENTICAL circles: will settle down.You understand?

P.S.

In everything the limit which uses Calculus is guilty.

Because this limit it is possible to give only presentation of VALUE of the DERIVATIVE but not the most derivative.

In Structural Analysis the absolute limit on accuracy for receiving derivative function instead of its value is used:

bob bundy wrote:

Please choose the following

base radius of cone

height of cone

number of slicesBob

Didn't understand. You look post #28 the most top line.

Give me the test.

"number of slices"

While you will have trapezes result will be approximate. As soon as you will take two areas of a circle

Bob

Try to translate by means of the dictionary start top from Russian. I here all accurately wrote all. I feel that my robot doesn't translate all sense of that that I want to inform you.

http://bolshoyforum.org/forum/index.php?topic=297286.0

I will try to explain a bean to you so. Present that on the plane there is circumference of any radius. ANY (! ! ! ) It is the line, it - not the area (! ! ! ) Now you to it add one more circumference in the same plane. Either it is more or has no value but such that between these two circumferences it was impossible to insert one more less.

It already area, instead of line. Elementary Square, the most smaller also is differential of the area of a circle. Any more line. But already area! It also is:

The sum of elementary segments of line (pieces) lying in one direction (not in parallel):

- is a line.

One point - One point it yet length not segment of line. Three points - not elementary. Integration is an absolute measure it doesn't depend on a unit of measure which the person can choose randomly.

You understand this?

P.S. I try to translate twice: from Russian into English then from English into Russian - sense is not adequate. I don't know what to do.

On this question:

"Why do you think this is ?"

you answered:

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

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

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:

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.

I think you know well what I mean..

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