Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,523

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.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

-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

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

Use the chain 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.**

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

That was funny, right?

**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.**

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

I mean about the chain rule. You did it!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

I use a package or a table.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

**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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

I am lost.

What technique should I use?

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

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

du = - sin(x) dx

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**zetafunc.****Guest**

Are you familiar with integration by substitution?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

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

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

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**zetafunc****Member**- Registered: 2014-05-21
- Posts: 87

He is trying to get you to notice that

for a certain f(x).

Offline