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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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

**In mathematics, you don't understand things. You just get used to them.**

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 437

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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.**

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100

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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.**

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Ok got it. Thanks

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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.**

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For example?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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.**

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Is it 0.3214?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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.**

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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

**In mathematics, you don't understand things. You just get used to them.**

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Hmm... shouldn't that be 0?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

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.**

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0.000375

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

I am getting error = 0.00075

**In mathematics, you don't understand things. You just get used to them.**

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Ok

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,654

Did you get all that?

**In mathematics, you don't understand things. You just get used to them.**

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