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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,106

Theoretically, Romberg should be much better than Simpson's.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

But, it is more complicated to program, though.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,106

You only need one column and the the formula generates all the rest.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

But, how do I know how many values to get for the first column?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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You do not. But like a difference table how far you go horizontally depends on how tall the first column is. Each column is more and more accurate, so pick a number n and go from there.

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Can anyone tell how to find the value of the following integral upto four significant digits with the help of a computer but not a readymade CAS?

J simulation:

```
load 'trig' NB. required for cos
samp =: 1000000 NB. the number of samples
avg =: +/%# NB. the average function
f =: ?samp$0 NB. random numbers in range (0,1)
fn =: cos f*pi%4 NB. get the list of cosines after scaling into range (0,pi/4)
fn100 =: fn^100 NB. get the 100th power
avg fn100*pi%4 NB. Take the average after multiplying (pi/4-0)
```

≈ 0.125139

which is close enough!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Isn't o. used for trig functions as well?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

trig functions must be loaded.

o.n is pi times n.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Only when monadic. As dyadic, it represents circle functions: http://www.jsoftware.com/help/dictionary/dodot.htm

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay, thanks, did not see that before!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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You're welcome.

The functions are hard to remember.

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**gAr****Member**- Registered: 2011-01-09
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Indeed, they are hard to remember and understand.

Anyway, it's good and quick once we get a hang of it. Their documentation is good, but scattered. They need to reorganize that.

E.g. I had to search for quite a long time to find how to change the array values

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I agree. Fortunately, the tutorials I found on that site are great!

How good are you with tacit expressions?

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Yes, and there are essays in that site with very useful programs!

I'm still learning. Are you too trying out J?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Yes, I've seen them. They are fantastic.

I have learned a bit about it, I was amazed by how simple and complex it looks at the same time. Also, the tacit programming part of J caught my eye. I haven't done much in it though.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay, tacit programming is the best part of the language.

But needs much practice to know the rules and use it efficiently.

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**anonimnystefy****Real Member**- From: The Foundation
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Yes, that is pretty much the reason why I could never do much in it.

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How do I evaluate this?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,106

What have you tried and although you have posted this in Computer math, I have to ask what method do you want?

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Hi Agnishom

You can use this fact:

I would not recommend it, though.

*Last edited by anonimnystefy (2014-05-21 20:04:36)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Here is an answer that uses Gaussian integration and has an error of approximately 10^-48

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

And the exact answer, given by M is:

*Last edited by anonimnystefy (2014-05-22 00:49:51)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,106

Hi;

Unless he wants an numerical integration method.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,609

Well, it is the exact answer even if he doesn't want it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,106

But he has M so why would he not do that himself?

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