# integrateit() -- simple naive one-dimensional R integration function

# by Jeffrey S. Rosenthal (www.probability.ca)

# Can integrate functions which are not "vectorised" for integrate()


integrateit = function(ff, themin=0, themax=1, N=1000) {
  if (themin >= themax)
    stop("Error: themin must be smaller than themax")
  xlist = themin + (0:N)*(themax-themin) / N
  thesum = 0.0
  for (i in 1:(N+1))
    thesum = thesum + ff(xlist[i])
  return( thesum * (themax-themin) / N )
}

# EXAMPLE:
f = function(x) {
      if (x<1/2) return(x^2)
      else return(x^3)
}
integrate(f,0,1)  # Gives error!
integrateit(f)
integrateit(f,0,1)
integrateit(f,-2,5)
integrateit(f,-2,5,10000)