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#51 2013-07-23 15:14:20

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

>>> integrate(f, 0, (3.141592653589793/4),4)
0.12645766198987884

Sweet Jesus, its still good enough


'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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#52 2013-07-23 15:17:39

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

Now for 5?


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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#53 2013-07-23 15:29:58

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

>>> for i in xrange(5,11):
	print integrate(f, 0, (3.141592653589793/4),i)

	
0.125091274611
0.125020215482
0.125018499911
0.125018481816
0.12501848174
0.12501848174

smile


'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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#54 2013-07-23 15:33:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

Hi;

You can empirically see that after n = 6 you have the 4 significant digits you require so that is the answer.


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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#55 2013-07-23 15:35:16

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
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Re: An Integral and the Computer

Yes. That is what I was planning to do.


'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

Online

#56 2013-07-23 15:38:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

When you get time check this page because your code is slightly off. There are implementations there that will help,

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


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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#57 2013-07-23 15:46:56

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

Why should it be off?

Thats just the formula...


'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

Online

#58 2013-07-23 15:54:28

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

You are probably out of alignment.

Try your formula out on this

f(x) = x^9 between 0 and 10 with 100000 intervals.

You should get 1000000000.75

After you do that I will show you one last thing that is really cute.


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

#59 2013-07-23 16:00:26

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
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Re: An Integral and the Computer

Yes. The correct answer should be 10^9.

Whats wrong with my code?


'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

Online

#60 2013-07-23 16:03:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

What did you get?


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

#61 2013-07-23 16:11:10

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
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Re: An Integral and the Computer

1000000000.7500005


'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

Online

#62 2013-07-23 16:26:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

That is correct!

This is a plot of what the trapezoid rule is doing for n = 10:

Notice it sometimes went over and sometimes under. The second trapezoid is almost perfect.

View Image: 2013-07-23_210011.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

#63 2013-07-23 16:54:31

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

What about post 58?

OK, see you later, gotta go to school

Last edited by Agnishom (2013-07-23 17:06:32)


'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

Online

#64 2013-07-23 17:15:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

Have a good day at school and study hard.

Post #62 was the cute thing. The program not only does the calculation but shows graphically what it did.


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

#65 2013-07-24 00:39:49

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

Thanks. School was good.

Why is that error occuring?


'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

Online

#66 2013-07-24 00:41:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

What error? I do not understand.


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

#67 2013-07-24 00:46:06

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

Read post 58 to 61


'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

Online

#68 2013-07-24 00:47:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

Hi;

It is possible there is a small problem with your code ( ever seen any code without bugs ?). But for the purposes of this discussion it worked well enough so I am happy.


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

#69 2013-07-24 00:56:57

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

Ofcourse there is some problem. Tell me where it is


'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

Online

#70 2013-07-24 02:42:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

What do you get for this problem here with n = 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

#71 2013-07-24 03:38:21

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

Which problem? I am getting confused..


'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

Online

#72 2013-07-24 03:39:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

The one that guy from India with the beard posted.


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

#73 2013-07-24 04:56:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

>>> for n in xrange(1,21):
	integrate(f, 0, (3.141592653589793/4),n)

	
0.3926990816987245
0.19649262597124922
0.13907218235606786
0.12645766198987884
0.12509127461149278
0.12502021548220082
0.12501849991109948
0.12501848181618283
0.12501848174029692
0.12501848174018745
0.12501848174018715
0.12501848174018718
0.12501848174018754
0.12501848174018773
0.12501848174018718
0.12501848174018768
0.12501848174018726
0.12501848174018754
0.12501848174018723
0.1250184817401873

'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

Online

#74 2013-07-24 05:05:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

Re: An Integral and the Computer

I am getting for n = 3, 0.15605651313635455


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

#75 2013-07-24 05:08:52

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,091
Website

Re: An Integral and the Computer

Why?

In that case, don't you think mine is better!


'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

Online

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