Asignación integrales

Nicolle Salamanca

Integrales

\[\int_{0}^{2e} ln(x)dx = \lim_{b \to 0}\int_{b}^{2e} ln(x)dx\]

curve(log(x),to=5,col="green",main="Áreas de la función ln(x) ")
abline(v=0, col= "gray")

abline(h=0, col= "gray")
abline(v=1, col="blue")

text(2.5,0.5,"Area 1",cex = 0.7)
text(0.38,-0.2,"Area 2",cex = 0.7)

log(exp(1))

[1] 1

puntos1 = 100000
d = c(); dn = c(); x = c(); y = c()
for(p in 1:puntos1){
  x[p] = runif(1, 1,2*exp(1))
  y[p] = runif(1, 0,log(2*exp(1)))
  d[p] = (y[p]<log(x[p]))
  dn[p] = ifelse(d[p] == T, 'Abajo', 'Arriba')
}

plot(x, y, col = ifelse(dn == 'Abajo', 'gray', 'darkblue'), pch = 19, cex = 0.25, main="ln(x) Cuadrante I")

puntos1 = table(dn)
(prop = puntos1[1]/sum(puntos1)) 

  Abajo 
0.63477 

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

[1] 5.436564

area1<-(area.simulada = area_total*prop);area1

    Area 
3.450968 

puntos2 = 100000
d = c(); dn = c(); x = c(); y = c()
for(p in 1:puntos2){
  x[p] = runif(1, 0,1)
  y[p] = runif(1, -10,0)
  d[p]= (y[p]<log(x[p]))
  dn[p] = ifelse(d[p] == T, 'Arriba', 'Abajo')
}
plot(x, y, col = ifelse(dn == 'Arriba', 'gray', 'darkblue'), pch = 19, cex = 0.25,main="ln(x) Cuadrante IV")

puntos2 = table(dn)
(prop = puntos2[1]/sum(puntos2))

  Abajo 
0.10018 

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

[1] 5.436564

area2<-(area.simulada = area_total*prop);area2

     Area 
0.5446349 

areatotal<-area1+area2
areatotal

    Area 
3.995602