[R] Odp: Integration in R

[Alaios]

Thanks a lot :)
Feeling embarassed !
Alex

--- On Mon, 1/10/11, Petr PIKAL <petr.pikal at precheza.cz> wrote:

> From: Petr PIKAL <petr.pikal at precheza.cz>
> Subject: Odp: [R] Integration in R
> To: "Alaios" <alaios at yahoo.com>
> Cc: r-help at r-project.org
> Date: Monday, January 10, 2011, 2:45 PM
> Hi
> 
> r-help-bounces at r-project.org
> napsal dne 10.01.2011 15:12:33:
> 
> > Dear all,
> > 
> > It has been   ages since I studied
> integration in college. Right now I 
> > try to recover all this kind of knowledge and then try
> to understand how
> >  integration works. 
> > 
> > 
> > 
> > Thus I am doing some first 'experiments' and I would
> like to request 
> your help
> > and comments.
> > 
> > 
> > 
> > I have the function:
> > 
> > 
> > 
> > p2<-function(x){0.5*(3*x^2-1)}
> > 
> > # I found the square of p2 by using some pencil and
> paper.
> > 
> > # The result is inside myfunc below
> > 
> > 
> > 
> > myfunc<- function(x) {0.25*(9*x^4+6*x^2+1)}
> 
> It is quite a long time I did school math but shouldn't be
> 
> myfunc<- function(x) {0.25*(9*x^4-6*x^2+1)}
>                
>            
>    ^^^^^
> myfunc<- function(x) {0.25*(9*x^4-6*x^2+1)}
> curve(myfunc,-1,1)
> integrate(p2sq,-1,+1)
> 0.4 with absolute error < 4.4e-15
> integrate(myfunc,-1,+1)
> 0.4 with absolute error < 4.4e-15
> 
> Regards
> Petr
> 
> 
> 
> > 
> > 
> > 
> > # Below I made R to find the square of p2
> > 
> > p2sq<-function(x) {p2(x) * p2(x)}
> > 
> > 
> > 
> > # Now I am trying to integrate both two function at
> the same interval. 
> #Both 
> > functions should denote the square of p2
> > 
> > 
> > 
> > integrate(p2sq,-1,+1)
> > 
> > # returns 0.4 with absolute error < 4.4e-15
> > 
> > 
> > 
> > integrate(myfunc,-1,+1)
> > 
> > # returns 2.4 with absolute error < 2.7e-14
> > 
> > 
> > 
> > if there is no error in my calculations could you
> please explain me why 
> > the two integrations return different results. Might
> be that I am 
> > missing something from the theory. I would like to
> thank you for your 
> > help
> > 
> > 
> > 
> > Regards
> > 
> > Alex
> > 
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> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained,
> reproducible code.
> 
>