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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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration with Inverse Trig function

Hi

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

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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.

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration with Inverse Trig function

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

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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! 

Bob

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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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration with Inverse Trig function

Hi bob

here's one for you:

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

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Integration with Inverse Trig function

hi Stefy

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

Bob

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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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration with Inverse Trig function

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

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Integration with Inverse Trig function

Latex corrected.

looking for a simplification.
B

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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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Integration with Inverse Trig function

How about

   ?

B

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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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration with Inverse Trig function

Where has e**x vanished?

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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.