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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

xSin(x^3)

pls help!

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Hi,

Are you sure it's sin(x^3) and not sin(x)^3 ?

If it's sin(x^3) , CAS gives the answer in terms of gamma function.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi nevinsmith;

gAr is right! have you posted the correct problem?

**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.**

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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

oh wait i missed out the definite integrals, its between pi and 0

the answers says 2pi/3

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi nevinsmith;

I am not getting that for that integral:

Is this what you want?

It should be this:

**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.**

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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

no it's not x(sinx)^3 or xsin^3x

it's xsin(x^3) brackets present in the question and x^3 inside the bracket

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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

could be a print error though

does the other one work out to be 2pi/3?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Something is wrong when it is x sin(x)^3 we get the answer you want. The other integral does not. Must be a typo in the question.

**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.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Yes, it's a print error!

The second integral shown by bobbym evaluates to 2*pi/3.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

oh right, but i still can't solve it

how do i integrate x(sinx)^3

techniques i've taught are- integration by parts, substitution, trignometric substitution, partial fractions and i think thats it

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Integration by parts should do 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.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Hi,

Use:

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

hi gar and bobbym thanks for helpin guys

I still can't do it

can you please show me step by step how to integrate?

using integration by parts? i can't seem to get rid of the integral it keeps getting bigger and bigger

do i set u' as (sinx)^3 or as x

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

hi nevinsmith

i think it should be u=x and dv=(sinx)^3 dx

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.

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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

This is what i can get up to

int xSinx^3 dx

set u=x u'=1

v'=sinx^3 integrate, v= cosx-1/3cosx^3

then integrate by parts

=xcosx-1/3xcosx^3 - int (cosx-1/3cosx^3)

i can't et rid of the integral!!

please help me!

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Hi,

Here it is:

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**nevinsmith****Member**- Registered: 2010-05-19
- Posts: 39

Hi Gar,

wow thank you so much!

thats so genious i would never think of that lol

thanks for the solution man!

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Hi nevinsmith,

You're welcome!

The properties of definite integrals are very useful, make most use of it.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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