Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Help log integration

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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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help log integration

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)

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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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help log integration

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)

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{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.}

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

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

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Malik

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help log integration

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

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{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.}

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

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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Malik

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help log integration

x+3>0
x+3-3>-3 by subtracting 3 from both sides.
x>-3
Is it O.K.?

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{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.}

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

ok thx

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

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

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help log integration

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

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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.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

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

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help log integration

Do you understand my answer in post #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.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

but in our book thick head method used

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help log integration

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help log integration

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.

is what you should have.

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

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{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.}

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

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

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Malik

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help log integration

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{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.}

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Help log integration

thx can you explain.it

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Malik

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help log integration

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

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{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.}