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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: 102,304

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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What is the integral of tan x?

'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'

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: 16,000

-ln(cos(x))+C.

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

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

'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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,304

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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?

'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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,304

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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: 102,304

I mean about the chain rule. You did it!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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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: 102,304

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.**

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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: 102,304

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.**

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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: 102,304

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.**

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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: 102,304

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.**

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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: 102,304

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.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,501

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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