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Integration in R

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Integration in R

alaios
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)}



# 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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Odp: Integration in R

PIKAL Petr
Hi

[hidden email] 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
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Integration in R

Ravi Varadhan
In reply to this post by alaios
You are missing basic algebra skills!  

You had:

myfunc<- function(x) {0.25*(9*x^4 + 6*x^2 + 1)}

This should be:

myfunc<- function(x) {0.25*(9*x^4 - 6*x^2 + 1)}


Ravi.
-------------------------------------------------------
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology School of Medicine Johns
Hopkins University

Ph. (410) 502-2619
email: [hidden email]

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On
Behalf Of Alaios
Sent: Monday, January 10, 2011 9:13 AM
To: [hidden email]
Subject: [R] Integration in R

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)}



# 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

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Odp: Integration in R

alaios
In reply to this post by PIKAL Petr
Thanks a lot :)
Feeling embarassed !
Alex

--- On Mon, 1/10/11, Petr PIKAL <[hidden email]> wrote:

> From: Petr PIKAL <[hidden email]>
> Subject: Odp: [R] Integration in R
> To: "Alaios" <[hidden email]>
> Cc: [hidden email]
> Date: Monday, January 10, 2011, 2:45 PM
> Hi
>
> [hidden email]
> 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
> >
> > ______________________________________________
> > [hidden email]
> mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained,
> reproducible code.
>
>




______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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