R help - Aug 2005 - integration

Hello

after reading few nodes from the info docs. I am not
sure  if this task can be done using R:
the density function f(x,y) = 12xy(1-y) for  
0<x<1, 0<y<1
the condition of inequality (x-y)> (1/2)
what if the limits of integration are functions of the
variable I am integrating over.
is this somthing which can be done in a simple way,
with R?
examples:
Mathimatic 5.1:
In[2]:=Integrate[12*x*y*(1-y)*Boole[x-y>1/2],{y,0,1},{x,0,1}]
Maple:
Doubleint(12*x*y*(1-y)*Heaviside(x-y-1/2),x=0..1,y=0..1);

many thanks

Numerical integration: yes.
Symbolic integration: no.

On Mon, 22 Aug 2005, Fred J. wrote:
> after reading few nodes from the info docs. I am not
> sure  if this task can be done using R:
> the density function f(x,y) = 12xy(1-y) for
> 0<x<1, 0<y<1
> the condition of inequality (x-y)> (1/2)
> what if the limits of integration are functions of the
> variable I am integrating over.
> is this somthing which can be done in a simple way,
> with R?
> examples:
> Mathimatic 5.1:
> In[2]:=Integrate[12*x*y*(1-y)*Boole[x-y>1/2],{y,0,1},{x,0,1}]
> Maple:
> Doubleint(12*x*y*(1-y)*Heaviside(x-y-1/2),x=0..1,y=0..1);
Symbolic integration: no.
Numerical integration: yes, e.g.

library(adapt)
adapt(2, c(0,0), c(1,1),
       functn=function(x) {y=x[2]; x=x[1]; 12*x*y*(1-y)*(x-y>1/2)})

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
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