object ArcParabLen {
  def lenCurve(n: Int): Double = {
    val h=(1/n.toDouble)
    def helper(acc:Double=0, x:Double, h:Double ):Double={
        if(x<=1){
          if(x<1&&(x+h)<=1) {
            val x1 = x + h
            val dX = x1 - x
            val dY = x1 * x1 - x * x
            val acc1 = acc+Math.sqrt(dX*dX+dY*dY)
            helper(acc1,x1,h)
          }
          else{
            val dX =1-x
            val dY =1-x*x
            val acc1 = acc+Math.sqrt(dX*dX+dY*dY)
            acc1
          }
        }
        else acc
      }
    helper(0, 0, h)
  }
}