4508.sagews

%r
##Integrales Dobles#
####################
IntDoble=function(f,li.e,ls.e,f.i.i,f.i.s){
u=runif(1000000,li.e,ls.e)
v=runif(1000000,f.i.i(u),f.i.s(u))
(ls.e-li.e)*mean(f(u,v)*(f.i.s(u)-f.i.i(u)))}

##Ejemplo##
f=function(x,y){1.5*(x^2+y^2)}
f1=function(x){1-x}
f2=function(x){1}
IntDoble(f,0,1,f1,f2)

[1] 0.7495188

n(integral(integral(1.5*(x^2+y^2),y,1-x,1),x,0,1))

0.750000000000000

%r
f=function(x,y){x-3*y}
f1=function(x){x}
f2=function(x){2*x}
IntDoble(f,0,1,f1,f2)

[1] -1.167652

var('y')
n(integral(integral(x-3*y,y,x,2*x),x,0,1))

-1.16666666666667