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
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 requestyour 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 > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code.
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: rvaradhan at jhmi.edu
-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of Alaios
Sent: Monday, January 10, 2011 9:13 AM
To: r-help at r-project.org
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
______________________________________________
R-help at r-project.org 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.