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#151 2013-07-27 20:08:10

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

To answer that we would need to cover the derivation of the error formula. That would require the Euler Mclaurin summation formula which would lead us on another discussion and is difficult.


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.

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#152 2013-07-27 20:27:09

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
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Re: An Integral and the Computer

is difficult

bobbym wrote:

If bobbym can, anyone can.


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#153 2013-07-27 20:30:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

Who said that fellow could do it.

The question is, do we spend the next 19 posts going over someone else's proof or do we spend it actually showing it work or in this case not 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.

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#154 2013-07-27 20:34:35

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

Bad Logic wrote:

If someone can do it, let him do it.
If no one can do it, how can I do it?

Good Logic wrote:

If someone can do it, I can do it too.
If no one can do it, I must do it.

Never mind, I think I will live long enough to get that proof. For now, tell me how to use it.


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#155 2013-07-27 20:40:19

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

I will cover a proof out of the book "Numerical Analysis" as soon as we do 2 examples.

Do you agree from post#147 that where the absolute value is a maximum is at x = 0?


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.

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#156 2013-07-27 20:41:28

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

yes!


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#157 2013-07-27 20:47:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

And what is that value? Remember it is an absolute value.


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.

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#158 2013-07-28 02:26:02

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: An Integral and the Computer

Hello

What about quadrature formulas that do not include the endpoints? What are the advantages of these and will you show one?

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#159 2013-07-28 02:41:49

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

Hi;

The ones that do not include the endpoints do that because for many integrals encountered in practice the endpoints are singularities. This creates problems for primitive languages.

No, I will not be doing any of them.


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.

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#160 2013-07-28 02:45:53

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

100


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#161 2013-07-28 02:51:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

Very good! Now we will just fill in the formula:

Let's pick n = 15.

The error is expected to be smaller or equal to .0228463.


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.

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#162 2013-07-29 02:49:30

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

Ok got it. Thanks


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#163 2013-07-29 04:43:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

Hi Agnishom;

Very good. Usually it works a lot better than that.


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.

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#164 2013-07-29 13:52:17

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

For example?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#165 2013-07-29 15:32:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

Supposing you had this integral instead:

What do you get from a trapezoidal rule with 5 panels?


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.

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#166 2013-07-30 01:42:38

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

Is it 0.3214?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#167 2013-07-30 03:16:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

Hi;

You will need a few more digits for thsi one because the error is quite small.

0.3214669303656079


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

#168 2013-07-30 03:34:37

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

Yes, I figured that those digits are not correct, so I truncated them


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#169 2013-07-30 03:59:45

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

This is the second derivative. We see that the maximum occurs at x = 1 and is about .25. Do you agree?

View Image: 2013-07-30_085603.gif

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

#170 2013-07-30 13:58:18

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

Hmm... shouldn't that be 0?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#171 2013-07-30 18:02:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

The integral is being evaluated in the interval 1 to 1.3


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

#172 2013-07-31 00:34:38

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

0.000375


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#173 2013-07-31 00:58:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

I am getting error = 0.00075


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.

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#174 2013-08-03 01:56:06

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,999
Website

Re: An Integral and the Computer

Ok


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#175 2013-08-03 02:00:20

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,730

Re: An Integral and the Computer

Did you get all that?


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

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