# [R] Integration in R

Alaios alaios at yahoo.com
Mon Jan 10 15:12:33 CET 2011

```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

```