[R] Odp: Integration in R

[Petr PIKAL]

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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