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curve(log(x), from = 1, to = 2*exp(1))

puntos = 1000000
d = c(); dn = c(); x = c(); y = c()
for(p in 1:puntos){
  x[p] = runif(1, 1, 2*exp(1))
  y[p] = runif(1, 0, 1.7)
  d[p] = (y[p]<log(x[p]))
  dn[p] = ifelse(d[p] == T, 'Abajo', 'Arriba')
}
plot(x, y, col = ifelse(dn == 'Abajo', 'darkgreen', 'darkblue'), pch = 19, cex = 0.25)

puntos = table(dn)
(prop = puntos[1]/sum(puntos)) # proporcion de puntos en el area

##    Abajo 
## 0.631913

names(prop) = 'Area'
(area_total = 2*exp(1))

## [1] 5.436564

a1=(area.simulada = area_total*prop)

curve(log(x), from =0, to = 1)

puntos = 1000000
d = c(); dn = c(); x = c(); y = c()
for(p in 1:puntos){
  x[p] = runif(1, 0, 1)
  y[p] = runif(1, -9, 0)
  d[p] = (y[p]>log(x[p]))
  dn[p] = ifelse(d[p] == T, 'Abajo', 'Arriba')
}
plot(x, y, col = ifelse(dn == 'Abajo', 'darkgreen', 'darkblue'), pch = 19, cex = 0.25)

puntos1 = table(dn)
(prop1 = puntos1[1]/sum(puntos1)) # proporcion de puntos en el area

##    Abajo 
## 0.111327

names(prop1) = 'Area'
(area_total1 = 1)

## [1] 1

a2=(area.simulada1 = area_total1*prop1)

sum(a1+a2)

## [1] 3.546762

puntos = 1000000

d = c(); dn = c(); x = c(); y = c();n = c();v=c();m = c(); x1= c()
for(p in 1:puntos){
  x[p] = runif(1, 0, 2*exp(1))
  y[p] = runif(1, -3.5, 0)
  d[p] = (y[p]>log(x[p]))
  dn[p] = ifelse(d[p] == T, "Arriba",'Abajo')
  
  x1[p] = runif(1, 0, 2*exp(1))
  v[p] = runif(1, 0, 1.7)
  m[p] = (v[p]<log(x1[p]))
  n[p] = ifelse(m[p] == T,"Arriba",'Abajo')
}

z=c(x1,x)
zz=c(v,y)
xxx=c(x,y)
xx=data.frame(n,dn,x,y,x1,v)
xa=  xx[which(xx$n=="Arriba"),-2]
xy =xx[which(xx$dn=="Arriba"),-1]
xaa=  xx[which(xx$n=="Abajo"),-2]
xyy =xx[which(xx$dn=="Abajo"),-1]


  plot(z,zz,pch = 20, cex = 0.25)
  points(xx$x,xx$y,cex=0.25,col ="darkblue",pch= 20)
  points(xx$x1,xx$v,cex=0.25,col ="darkgreen",pch= 20)
  points(xa$x1,xa$v,cex=0.25,col ="darkgreen",pch= 20)
  points(xa$x,xa$y,cex=0.25,col ="darkgreen",pch= 20)
  points(xy$x,xy$y,cex=0.25,col ="darkgreen",pch= 20)
 
  points(xaa$x1,xaa$v,cex=0.25,col ="darkblue",pch= 20)
  points(xyy$x,xyy$y,cex=0.25,col ="darkblue",pch= 20) 

puntos3 = table(dn)
(prop3 = puntos3[1]/sum(puntos3)) # proporcion de puntos en el area

##    Abajo 
## 0.949114

names(prop1) = 'Area'
(area_total3 = 1)

## [1] 1

a3=(area.simulada3 = area_total3*prop3)


puntos4 = table(n)
(prop4 = puntos4[2]/sum(puntos4)) # proporcion de puntos en el area

##   Arriba 
## 0.515661

names(prop4) = 'Area'
(area_total4 = 2*exp(1))

## [1] 5.436564

a4=(area.simulada4 = area_total4*prop4)


sum(a3+a4)

## [1] 3.752538