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That is okay

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 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: 90,607

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

**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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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 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: 90,607

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

**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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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 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: 90,607

Here is the difference in the two methods.

**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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Impressive...

'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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Are you sure it starts with h/3?

Besides, how is the same thing as drawing curves?

'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: 90,607

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.**

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'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: 90,607

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

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

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So, should I program it?

'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: 90,607

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

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

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```
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
```

'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: 90,607

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.**

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I am getting that too.

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

'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: 90,607

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

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

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

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

'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: 90,607

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.**

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Why will integration problems come to me in the reality?

Could you explain how you got that formula?

'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: 90,607

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.**

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hahaha

okay

'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: 90,607

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.**

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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.

'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: 90,607

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

Here is the best image I have so far.

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

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