[R] 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