### <code r>
# dvg <- function(x, ts, tr, a, n) {tr+(ts-tr)/((1+(a*x)^n)^(1-1/n))}
dvg <- function(x){0.23+(0.64-0.23)/((1+(1.22*x)^1.34)^(1-1/1.34))}
dvg(10) - dvg(1500) # [1] 0.1417496
integrate(dvg, lower = 10, upper = 1500)
# 412.4841 with absolute error < 0.0011
# emprestando a função para cálculo da área abaixo da curva já postada por Walmes Zeviani
aac <- function(x, y){
ox <- order(x)
x <- x[ox]
y <- y[ox]
alt <- diff(x)
bas <- y[-length(y)]+diff(y)/2
a <- sum(alt*bas)
return(a)
}
x=seq(10,1500, by=10); y=dvg(x); aac(x, y) #[1] 412.5297
x=seq(10,1500, by=1); y=dvg(x); aac(x, y) #[1] 412.4846
x=seq(10,1500, by=.1); y=dvg(x); aac(x, y) #[1] 412.4841
integrate(dvg, lower = 10, upper = 1500)
# 412.4841 with absolute error < 0.0011
### visualização
plot(x, y, ylim=c(0,.5), type='n')
polygon(c(x[1],x,x[length(x)]),c(0,y,0), col=5)
points(c(10,1500), c(dvg(10), dvg(1500)), col=2, pch=20)
text(c(10,1500), c(dvg(10), dvg(1500)), round(c(dvg(10), dvg(1500)),4), cex=.5, pos=3)
### </code>