Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2011-07-23 22:44:06

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

how do i integrate this?

xSin(x^3)

pls help!

Offline

#2 2011-07-23 23:01:25

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

Re: how do i integrate this?

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."

Offline

#3 2011-07-23 23:29:12

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

Re: how do i integrate this?

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.

Offline

#4 2011-07-23 23:56:07

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

Re: how do i integrate this?

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

the answers says 2pi/3

Offline

#5 2011-07-23 23:59:20

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

Re: how do i integrate this?

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.

Offline

#6 2011-07-24 00:03:06

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

Re: how do i integrate this?

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

Offline

#7 2011-07-24 00:04:21

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

Re: how do i integrate this?

could be a print error though

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

Offline

#8 2011-07-24 00:05:17

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

Re: how do i integrate this?

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.

Offline

#9 2011-07-24 00:08:08

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

Re: how do i integrate this?

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."

Offline

#10 2011-07-24 00:19:12

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

Re: how do i integrate this?

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

Offline

#11 2011-07-24 00:21:37

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

Re: how do i integrate this?

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.

Offline

#12 2011-07-24 00:22:25

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

Re: how do i integrate this?

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."

Offline

#13 2011-07-24 00:31:22

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

Re: how do i integrate this?

hi gar and bobbym thanks for helpin guys

I still can't do it sad

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

Offline

#14 2011-07-24 00:33:49

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

Re: how do i integrate this?

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.

Offline

#15 2011-07-24 00:44:53

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

Re: how do i integrate this?

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!

Offline

#16 2011-07-24 00:53:48

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

Re: how do i integrate this?

Hi,

Here it is:


"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."

Offline

#17 2011-07-24 00:56:53

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

Re: how do i integrate this?

Hi Gar,

wow thank you so much!
thats so genious i would never think of that lol

thanks for the solution man!

Offline

#18 2011-07-24 01:03:40

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

Re: how do i integrate this?

Hi nevinsmith,

You're welcome!

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


"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."

Offline

Board footer

Powered by FluxBB