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#1 2012-03-04 20:49:50

Kryptonis
Member
Registered: 2011-03-03
Posts: 11

Integration with Inverse Trig function

I'm having a bit of a time with this. I have tried integration by parts and just can't seem to get it right....

∫(3-3x)/(sqrt(64-9x^2)) dx

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#2 2012-03-04 20:58:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Integration with Inverse Trig function

Hi

Use the substitution u=8*sin(x)/3


“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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#3 2012-03-06 14:46:24

Kryptonis
Member
Registered: 2011-03-03
Posts: 11

Re: Integration with Inverse Trig function

Thanx a bunch, was totally going in the wrong direction on this

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#4 2012-03-06 21:02:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Integration with Inverse Trig function

If there's anything else you don't understand,ask freely over here.


“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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#5 2012-03-30 19:11:54

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Integration with Inverse Trig function

hi brabenderjack

Welcome to the forum!

Speaking personally, I don't think there is a guaranteed way of doing integration.  With differentiation, once you can do the basic functions (powers, trig, exp, log) and you can do product, quotient and chain rule, you can differentiate anything made up from these.

But there's no such approach for integration.

Sometimes it is 'obvious' that it is a certain function just by looking and remembering the rules for differentiation. 

Sometimes it 'looks' like integration by parts may work.

If I see the presence of a function and its derivative then I know substitution will help.

Some other problems also 'yield' to substitution.

Beyond that, it's just trial and improvement for me.

Usually, for exams, the examiners only set ones that can be done by one of the above methods.

There are some fairly simple looking functions that won't give a 'nice' answer at all!

If I got one I could not do, I'd post it here!  smile

Bob


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

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#6 2012-03-30 22:47:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Integration with Inverse Trig function

Hi bob

here's one for you:

Last edited by anonimnystefy (2012-03-30 22:53:03)


“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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#7 2012-03-31 01:28:52

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Integration with Inverse Trig function

hi Stefy

just a bit of 'light relief' before I go back to your sequence.

Bob


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

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#8 2012-03-31 01:30:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Integration with Inverse Trig function

As i gathered from your LaTeX code that looks right,but there is a simpler form.


“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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#9 2012-03-31 01:35:46

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Integration with Inverse Trig function

Latex corrected.

looking for a simplification.
B


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

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#10 2012-03-31 01:39:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Integration with Inverse Trig function

How about

   ?

B


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

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#11 2012-04-28 13:41:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Integration with Inverse Trig function

Where has e**x vanished?


“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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