Math Is Fun Forum

amberzak

Member

Registered: 2012-03-16

Posts: 80

Intergrating a function with partial fractions - calculus

Can you please take me through this question step by step please:

As usual I've been given the answer, but need to show steps to get there
(my teacher does know I get help on here, as I write about it in my reflection sheet)

I can post the answer if you like?

Last edited by amberzak (2012-05-15 01:12:27)

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Don't think outside the box. Think there is no box

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Intergrating a function with partial fractions - calculus

Hi;

Substitute values into x to form a 2X2 simultaneous set.

Using x = 1 and x = 0 you will get:

A = 2

B = 2

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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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Intergrating a function with partial fractions - calculus

Multiply by 3-2x and substitute x=2/3 to get B. Multiply by 3+2x and substitute x=-2/3 to get A.

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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.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Intergrating a function with partial fractions - calculus

It's Calculus, so the answer is:

How do we get there?

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Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Intergrating a function with partial fractions - calculus

Use the rule ∫ u(x)+v(x) dx= ∫ u(x) dx + ∫ v(x) dx.

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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.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Intergrating a function with partial fractions - calculus

I've never seen the x with the arrow before. What does it mean?

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Don't think outside the box. Think there is no box

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Intergrating a function with partial fractions - calculus

Hi;

That means maps to. In this case you might use it as a synonym for function.

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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.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Intergrating a function with partial fractions - calculus

Okay. so the first thing I need to do is find A and B as shown above?

Then, how do I integrate the fraction. My teacher said it was something to do with Partial Fractions, and did say if i couldn't do the question not to worry because I've not studied partial fractions before, but I would like to at least understand how the answer is derived.

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Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Intergrating a function with partial fractions - calculus

Try using the partial fractions to split it into two integrations.

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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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Intergrating a function with partial fractions - calculus

Hi amberzak;

Did you follow how the partial fractions were found?

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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.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Intergrating a function with partial fractions - calculus

No, not really. Could you please go through that? I kind of see it.

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Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Intergrating a function with partial fractions - calculus

Hi amberzak

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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.