Math Is Fun Forum

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: basic calculus

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

What is the integral of tan x?

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'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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: basic calculus

-ln(cos(x))+C.

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“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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

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

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: basic calculus

Use the chain rule.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

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?

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: basic calculus

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

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

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

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

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

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: basic calculus

I use a package or a table.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc.

Guest

Re: basic calculus

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

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

Then?
Please continue

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: basic calculus

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

I am lost.

What technique should I use?

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: basic calculus

du = - sin(x) dx

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

But why are you doing this?
I wanted an interation of it

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'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.

zetafunc.

Guest

Re: basic calculus

Are you familiar with integration by substitution?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

I think I can do it now.
I will try the next time I wake up

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

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 (2014-05-25 22:26:29)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: basic calculus

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

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'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.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: basic calculus

He is trying to get you to notice that

for a certain f(x).