# Integration in R

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## 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-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Odp: Integration in R

 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-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.