# [R] Integration in R

Berend Hasselman bhh at xs4all.nl
Tue Jan 8 22:00:35 CET 2013

```On 08-01-2013, at 19:51, Naser Jamil <jamilnaser79 at gmail.com> wrote:

> Thanks. But then how to implement condition like 0<x1<x2<7? I would be
> happy to know that.
>

David implemented the condition by multiplying by x[1]<x[2] which in a numeric context is 0 when x[1]<x[2] en 1 when x[1]>=x[2]. That is what your requirement does.
The condition 0<x1<x2<7 has been split into three separate parts

0<x1<7
0<x2<7
x1<x2

The first two can be converted to arguments of adaptIntegrate.
The last is inserted into the function definition effectively making the function return 0 when x1>x2 which is what your inequality implies.

Berend

> On 8 January 2013 18:41, David Winsemius <dwinsemius at comcast.net> wrote:
>
>>
>>
>> On Jan 8, 2013, at 10:27 AM, Naser Jamil wrote:
>>
>> Hi David,
>>> x[2] is the second variable, x2. It comes from the condition 0<x1<x2<7.
>>>
>>
>> No, it doesn't come from those conditions. It is being grabbed from some
>> "x"-named object that exists in your workspace.
>>
>> If your limits were 7 in both dimensions, then the code should be:
>>
>> adaptIntegrate(f, lowerLimit = c(0, 0), upperLimit = c(7,7))
>> #----
>> \$integral
>> [1] 228.6667
>>
>> (At this point I was trusting R's calculus abilities more than yours. I
>> wasn't too trusting of mine either, and so tried seeing if Wolfram Alpha
>> would accept this expression:
>> integrate 2/3 (x+y) over 0< x<7,  0<y<7
>>
>> ; which it did and calculating the decimal expansion of the exact fraction:
>>
>>> 686/3
>> [1] 228.6667
>>>
>>
>> --
>> David.
>>
>>
>>
>>
>>> Thanks.
>>>
>>> On 8 January 2013 18:11, David Winsemius <dwinsemius at comcast.net> wrote:
>>>
>>> On Jan 8, 2013, at 9:43 AM, Naser Jamil wrote:
>>>
>>> Hi R-users.
>>>
>>> I'm having difficulty with an integration in R via
>>> the package "cubature". I'm putting it with a simple example here.  I wish
>>> to integrate a function like:
>>> f(x1,x2)=2/3*(x1+x2) in the interval 0<x1<x2<7. To be sure I tried it
>>> by hand and got 114.33, but the following R code is giving me 102.6667.
>>>
>>> ------------------------------**------------------------------**-------
>>> library(cubature)
>>> f<-function(x) { 2/3 * (x[1] + x[2] ) }
>>> adaptIntegrate(f, lowerLimit = c(0, 0), upperLimit = c(x[2],7))
>>>
>>>
>>> What is x[2]?  On my machine it was 0.0761, so I obviously got a
>>>
>>> --
>>> David Winsemius, MD
>>> Alameda, CA, USA
>>>
>>>
>>>
>> David Winsemius, MD
>> Alameda, CA, USA
>>
>>
>
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