|
|
| View previous topic :: View next topic |
| Author |
Message |
Magician
Guest
|
 Posted: Fri Jul 11, 2008 11:50 pm Post subject: integral defination |
 |
|
what is the integral
Limit e ->0 [ Integral { F(x) , 0, e} }
i.e what is the value of the integral if the two limita approach each
other ? |
|
| Back to top |
|
 |
| |
Ads |
Advertising
Sponsor
|
|
smn
Guest
|
| Posted: Sat Jul 12, 2008 12:42 am Post subject: Re: integral defination |
|
|
On Jul 11, 4:50 pm, Magician <jadoo.d...@gmail.com> wrote:
| Quote: |
what is the integral
Limit e ->0 [ Integral { F(x) , 0, e} } =0
i.e what is the value of the integral if the two limita approach each
other ?
|
Say that the absolute value of F(x) is bounded by M ,Then the the
absolute value of youy integral is bounded by M(e-0) --> M0=0 as e --
>0 .Regards,smn |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
Magician
Guest
|
| Posted: Sat Jul 12, 2008 11:10 pm Post subject: Re: integral defination |
|
|
Well actually, in my case F(x) is not bounded. so the integral must
have a finite value.
Sorry for not properly framing the question. Can i treat this problem
in some way? |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
smn
Guest
|
| Posted: Sun Jul 13, 2008 10:07 pm Post subject: Re: integral defination |
|
|
On Jul 12, 4:10 pm, Magician <jadoo.d...@gmail.com> wrote:
| Quote: |
Well actually, in my case F(x) is not bounded. so the integral must
have a finite value.
Sorry for not properly framing the question. Can i treat this problem
in some way?
|
What level are you at,I mean is this calculus or real variables.For
unbounded functions the answer is still 0 but the proof uses
convergence theorems usually done for the more general Lebesgue
integral .Specifically since the absolute value of the integral is
less or equal to the integral of the absolute value it suffices by
replacing F by |F| to assume F is non-negative and integrable over say
the interval from 0 to 1 ,Let F_n (x)= F(x) if 0<x<=e and F_n(x)=0 for
e<x<=1 .then F_n (x) is a non increasing sequence of functions
tending to 0 at each fixed x in 0<x<=1 .The monotone convergence
theorem says that the integral from 0 to 1 of F_n tends to 0 as n--
| Quote: |
0 .But int0,1of F_n = int0,e of F so this gives your needed result .
The monotone convergence theorem is not something you can prove by |
yourself in calculus ,How ever if you are dealing with an improper
integral of some F continuous on 0<x <=1 but with F(x)increasing to 00
as x tends to 0 you might handle it by looking at the integral d,e of
F and bounding it from above ,smn |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
