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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

Hi

Integral ln|x+3| range from 5 to -1 how solve this please help how we work with absolute value

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,133

Hi;

how we work with absolute value

One idea is to just get rid of it. In the interval of integration -1 to 5, log(abs(x+3)) = log(x+3)

**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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**thickhead****Member**- Registered: 2016-04-16
- Posts: 982

Hi Zeeshan 01,

For absolute values first you have to find out which expression for which domain.

In this case,

|x+3| = -x-3 for -∞ <x <=-3

=x+3 for -3<=x<-∞

In this it falls in the second part of the domain but suppose the intgration is from -5 to -1 then

*Last edited by thickhead (2016-08-25 17:28:37)*

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

|x+3| = -x-3 for -∞ <x <=-3 please.explain it

Math !!!!.

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 982

By definition |x+3|= x+3 if x+3>0 i.e. x>-3 and

=-(x+3) if x+3<0 i.e. x<-3

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

i understand absolute values that if |x+3|= x+3 if x+3>0 but how 3 comes.in. your interval

and how we work with it i know how to take definite intervals but this question i dont understand properly

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 982

x+3>0

x+3-3>-3 by subtracting 3 from both sides.

x>-3

Is it O.K.?

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

ok thx

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

i m not asking about this i m asking how ro put intervals.in intrgral

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,133

What do you mean? Put them in latex? Solve the integral with them?

**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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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

no you dont understand my question i am asking i give interval from 5 to -1 how its intervals become -3 to -5 and -1 to -3 as mention above plz tell

Math !!!!.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,133

Do you understand my answer in post #2?

**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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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

but in our book thick head method used

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,133

I would just drop the abs, since you do not like that way you will have to wait.

**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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**thickhead****Member**- Registered: 2016-04-16
- Posts: 982

Zeeshan 01 wrote:

no you dont understand my question i am asking i give interval from 5 to -1 how its intervals become -3 to -5 and -1 to -3 as mention above plz tell

Hi zeeshan 01,

I was giving you a hypothetical case.

In your case x from 5 to -1 , -3 never comes in. |x+3| remains x+3 throughout your interval. Sorry for any confusion caused to you.Bobbym's view is perfect and to the point. Please follow him.

*Last edited by thickhead (2016-08-27 18:18:53)*

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

Ok thx but if question is ln|x-3| I DO SAME work????

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 982

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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**Zeeshan 01****Member**- Registered: 2016-07-22
- Posts: 317

thx can you explain.it

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 982

In the domain (-1,5) |x+3|=x+3 That is all.

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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