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#101 2013-07-25 02:49:00

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
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Re: An Integral and the Computer

That is okay smile

By the way, It is going to be a couple of hours before I sleep. The time here is 20:18 PM


'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 made a human being happy! There is no further achievement.' -bobbym

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#102 2013-07-25 02:49:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

Early night. I will begin preparing what I know about it.


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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#103 2013-07-25 03:01:05

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
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Re: An Integral and the Computer

Whats your time now?


'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 made a human being happy! There is no further achievement.' -bobbym

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#104 2013-07-25 03:02:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

8:00 am and soon I will be going offline.


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.

Online

#105 2013-07-25 03:19:29

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

OK Have a good day


'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 made a human being happy! There is no further achievement.' -bobbym

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#106 2013-07-25 03:20:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

Here is the difference in the two methods.

View Image: 220px-Simpsons_method_illustration.png View Image: 220px-Trapezoidal_rule_illustration.png

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.

Online

#107 2013-07-25 05:10:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

Impressive...


'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 made a human being happy! There is no further achievement.' -bobbym

Online

#108 2013-07-25 16:04:42

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

Are you sure it starts with h/3?

Besides, how is the same thing as drawing curves?


'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 made a human being happy! There is no further achievement.' -bobbym

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#109 2013-07-25 16:05:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

Sorry, we were both posting at the same time and I could not edit fast enough.

The basic formula looks like this:

with

h = (b-a)/n

x_i = a + i*h


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.

Online

#110 2013-07-26 00:43:16

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

up


'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 made a human being happy! There is no further achievement.' -bobbym

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#111 2013-07-26 00:58:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

It's convergence is much faster than the trapezoidal rule.


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.

Online

#112 2013-07-26 01:18:09

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

So, should I program 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 made a human being happy! There is no further achievement.' -bobbym

Online

#113 2013-07-26 01:19:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

If you like, then we will see if our answers compare.


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.

Online

#114 2013-07-26 01:36:33

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

def integrate(f, a, b, n):
	h = float(b-a)/n
	x = lambda i: (a + i*h)
	s1 = 0
	for j in xrange(1,(n/2)):
		s1 += f(x(2*j))
	s1 *= 2
	s2 = 0
	for j in xrange(1,(n/2)+1):
		s2 += f(x(2*j - 1))
	s2 *= 4
	s = h/3*(f(x(0)) + f(x(n)) + s1 + s2)
	return s

'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 made a human being happy! There is no further achievement.' -bobbym

Online

#115 2013-07-26 01:42:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

Let's try it on your integral with n =30.

I got .12501848174018723 using an M and a procedural program.

What did you get?


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.

Online

#116 2013-07-26 04:07:56

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

I am getting that too.

The sad part is that I did not get the feeling of making the curves. sad . It was sort of dry...


'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 made a human being happy! There is no further achievement.' -bobbym

Online

#117 2013-07-26 04:10:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

I could make a drawing for you later that might help.


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.

Online

#118 2013-07-26 04:14:21

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

That I can do for myself with a lot more colors than you would use wink xD

Never mind, but the formula at post 109 is not looking like a curve or giving a feeling of it. Sadly, it works...


'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 made a human being happy! There is no further achievement.' -bobbym

Online

#119 2013-07-26 04:20:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

You have a nice program that you can use later on to integrate functions that you will not be able to do by hand and there will ne lots of them.


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.

Online

#120 2013-07-26 04:24:25

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

Why will integration problems come to me in the reality?

Could you explain how you got that 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'
'You made a human being happy! There is no further achievement.' -bobbym

Online

#121 2013-07-26 04:26:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

Integration is the area under a curve. They come up in physics and probability a lot.

I copied it. It is in many books and also on Wikipedia.


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.

Online

#122 2013-07-26 04:29:22

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

hahaha big_smile

okay


'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 made a human being happy! There is no further achievement.' -bobbym

Online

#123 2013-07-26 04:30:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

I figured you wanted a real formula and not a bobbym creation.


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.

Online

#124 2013-07-26 04:34:33

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
Website

Re: An Integral and the Computer

Nope. I want something that gives me the geometric feeling of the area. It can be anything, a program or a formula or some philosophy.


'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 made a human being happy! There is no further achievement.' -bobbym

Online

#125 2013-07-26 04:35:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: An Integral and the Computer

I looked at two geogebra programs but they were not very impressive.

Here is the best image I have so far.

image003.gif


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.

Online

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