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#26 2013-06-18 01:23:12

ShivamS
Member
Registered: 2011-02-07
Posts: 3,415

Re: basic calculus

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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#27 2013-06-18 01:27:00

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#28 2013-06-22 05:17:03

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

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

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#29 2013-06-22 05:18:52

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,847

Re: basic calculus

-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

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#30 2013-06-22 05:33:09

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

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

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#31 2013-06-22 05:40:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

Use the chain rule.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#32 2013-06-22 05:54:59

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

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

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#33 2013-06-22 05:58:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

That was funny, right?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#34 2013-06-22 06:03:46

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

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


'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

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#35 2013-06-22 06:04:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

I mean about the chain rule. You did it!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#36 2013-06-22 06:06:50

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

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

Achchha, 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

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#37 2013-06-22 06:08:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

I use a package or a table.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#38 2013-06-22 06:10:24

zetafunc.
Guest

Re: basic calculus

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

#39 2013-06-22 06:13:06

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

zetafunc. wrote:

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

Then?
Please continue


'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

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#40 2013-06-22 06:15:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

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


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#41 2013-06-22 06:18:56

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

I am lost.

What technique should I use?


'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

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#42 2013-06-22 06:22:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

du = - sin(x) dx


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#43 2013-06-22 06:28:51

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

But why are you doing this?
I wanted an interation of 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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#44 2013-06-22 06:29:20

zetafunc.
Guest

Re: basic calculus

Are you familiar with integration by substitution?

#45 2013-06-22 06:29:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#46 2013-06-22 06:39:54

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

I think I can do it now.
I will try the next time I wake 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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#47 2013-06-22 06:43:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,749

Re: basic calculus

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#48 2014-05-25 22:20:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,124

Re: basic calculus

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

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#49 2014-05-26 05:08:30

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: basic calculus

Why is tan(x) = ln(f(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

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#50 2014-05-26 07:51:51

zetafunc
Member
Registered: 2014-05-21
Posts: 77

Re: basic calculus

He is trying to get you to notice that

for a certain f(x).

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