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 

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. 

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

From: Petr PIKAL <petr.pikal at precheza.cz>
Subject: Odp: [R] Integration in R
To: "Alaios" <alaios at yahoo.com>
Cc: r-help at r-project.org
Date: Monday, January 10, 2011, 2:45 PM
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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