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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

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

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

But, it is more complicated to program, though.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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
- Posts: 86,676

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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?

"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
- Posts: 15,525

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

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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**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
- Posts: 15,525

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
- Posts: 3,479

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

"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
- Posts: 15,525

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?

"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
- Posts: 15,525

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.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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
- Posts: 86,676

Here is an answer that uses Gaussian integration and has an error of approximately 10^-48

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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: 86,676

Hi;

Unless he wants an numerical integration method.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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: 86,676

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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