Dear R experts,
I computed the same integral in two different ways, and find different
values in R.
The difference is due to the max function that is part of the integrand. In
the first case, I keep it as such, in the second case, I split it in two
depending on the values of the variable of integration.

1) First computation

# Function g
g<-
function(x){1/(x*0.20*sqrt(10)*sqrt(2*pi))*exp(-0.5*((log(x/50)-0.1*10)/(0.20*sqrt(10)))^2)}

####### Function f1
f1<- function(x) {1/(5000000+100000*x+10000*max(x-50,0))}

integrand1<- function(x) {
  out<- f1(x)*g(x)
  return(out)
}

i2<- integrate(integrand1, lower=0, upper=Inf )$value

It gives me: i2=  3.819418e-08

2) Second computation
I break the max function in two, depending on the values of the variable of
integration x (and I use the same density g as before):

f11<- function(x) {1/(5000000+100000*x)}
f12<- function(x) {1/(5000000+100000*x+10000*(x-50))}


integrand11<- function(x) {
  out<- f11(x)*g(x)
  return(out)
}

integrand12<- function(x) {
  out<- f12(x)*g(x)
  return(out)
}


i21<- integrate(integrand11, lower=0, upper=50 )$value
+integrate(integrand12, lower=50, upper=Inf)$value

I get i21=5.239735e-08

The difference makes a huge difference for the computations I do. Does
anyone know where it comes from?
Thanks in advance!

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