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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

I agree that there is a lot of maths in computer science, however majority of the programmers nowadays are not very aware of that. They go into programming for a good job and nothing else.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

The people who are paying them are the ones that need an education. Is it the boys at Redmond?

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What is the integral of tan x?

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

I'm not crazy, my mother had me tested.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

-ln(cos(x))+C.

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

The knowledge of some things as a function of age is a delta function.

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or rather ln(sec(x)) + C.

Now, how do you differentiate ln(sec(x)) step by step. I guess there is a substitution method

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

Use the chain rule.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Let y = log(sec(x)) and u = sec(x)

Clearly, du/dx = sec(x)tan(x)

and, dy/du = 1/u = 1/sec(x)

Therefore, (du/dx)*(dy/du)= dy/dx = tan(x)

What is chain rule?

Anyhow, how do I integrate tan(x) by hand?

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

That was funny, right?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Math is Fun. I am not sure if it is funny

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

I mean about the chain rule. You did it!

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Ha ha ha! So, thats called the chain rule!

Achchha, how do I integrate tan(x) by hand?

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

I use a package or a table.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**zetafunc.****Guest**

Write tan(x) = sin(x)/cos(x).

zetafunc. wrote:

Write tan(x) = sin(x)/cos(x).

Then?

Please continue

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

That is the first step. Set u = cos(x)

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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I am lost.

What technique should I use?

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

du = - sin(x) dx

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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But why are you doing this?

I wanted an interation of it

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

I'm not crazy, my mother had me tested.

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**zetafunc.****Guest**

Are you familiar with integration by substitution?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

Because you are already done! Look at the numerator and what du equals.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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I think I can do it now.

I will try the next time I wake up

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,325

See the sin(x) dx? Well you have du = - sin(x) dx and u = cos(x)

You get -du/u, which you can certainly integrate.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

hi Agnishom,

This old post popped up today because of a spammer but I have an answer which might be useful for this:

http://www.mathisfunforum.com/viewtopic.php?pid=316853#p316853

Achchha, how do I integrate tan(x) by hand?

If you start with

and differentiate, you get:

So, when integrating, it is always worth being on the lookout for the presence of a function and its derivative. In your question we have both sine and cosine x , so we do have the function (cos) and its derivative (sin)

By inspection I can see I'm going to need a minus sign too, thus:

A similar argument works for this one:

Substitution for f(x) will always work in these cases (can you see why?) but it takes longer.

Bob

ps. Sometimes I can see an integration 'by inspection'. It's an acceptable method provided you 'prove' your 'guess' actually works by differentiation.

*Last edited by bob bundy (2014-05-25 22:26:29)*

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Why is tan(x) = ln(f(x))?

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

I'm not crazy, my mother had me tested.

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He is trying to get you to notice that

for a certain f(x).

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