Coding is a social activity - This was coded by me and a friend some lazy afternoon while drinking beer. This is a script which calculates the path integral for a function (does so horrible wrong now though).

Path intergral

import java.math._

def calculatePoints(xvals: List[Double], func: Double=> (Double,Double) ) = xvals.map{ x => func(x)}

def calculateLengthOfPoints(points: List[(Double,Double)], length: Double): Double = {
  def distance(p1: (Double,Double), p2: (Double,Double)) = 
    Math.sqrt(Math.pow(p2._1-p1._1,2)+Math.pow(p2._2-p1._2,2))
  points match {
    case Nil => length
    case point::rest if rest == Nil => calculateLengthOfPoints(rest, length)
    case point::rest => calculateLengthOfPoints(rest, length+distance(point,rest.first))
  }
}

def calculateLengthOfFunctionInInterval(func: Double => Double, startX: Double, endX: Double) = {
  val points = calculatePoints( (startX to endX).by(1).toList, (x) => (x,func(x)))
  calculateLengthOfPoints(points, 0)
}

def calculateLengthOfFunctionInInterval2(func: Double => Double, startX: Double, endX: Double, stops: Int) = {
  
  val xValues = {
    val step = (endX - startX + 1.0) / stops
    def increment(x: Double): Double = startX + (x*step)
    vals = (0 to stops-1).toList.map { _ match {
      case 0 => startX
      case x if x == stops-1 => endX
      case x => increment(x)
    }} 
  }

  val points = calculatePoints( xValues, x => (x,func(x)))
  calculateLengthOfPoints(points, 0)
}