Arc length

The underlying JavaScript code

<jsxgraph width="800" height="400" box="box">
var brd = JXG.JSXGraph.initBoard('box', {axis:true, originX: 400, originY: 300, grid:true, unitX: 50, unitY: 50});
var n = brd.createElement('slider',[[1,3],[5,3],[1,10,50]],{name:'n'});
var f = function(x){ return 0.2*x*x+2.0*Math.sin(x); }
var plot = brd.createElement('functiongraph',[f], {strokeWidth:1,strokeOpacity:0.3});
var start = -3.0;
var end = 5.0;
var sc = brd.createElement('curve',[[0],[0]],{dash:1,strokeWidth:1,strokeColor:'red'});
sc.updateDataArray = function() {
   var i;
   var m = n.Value();
   m = Math.floor(m);
   var d = (end-start)/m;
   this.dataX = [];
   this.dataY = [];
   this.dataX[0] = start;   
   this.dataY[0] = f(start);   
   for (i=1;i<=m;i++) {
     this.dataX.push(start+i*d);   
     this.dataY.push(f(start+(i-1)*d));   
     this.dataX.push(start+i*d);   
     this.dataY.push(f(start+i*d));   
   }  
}
var approx = brd.createElement('curve',[[0],[0]], {strokeColor:'red'});
approx.updateDataArray = function() {
   var i;
   var m = n.Value();
   m = Math.floor(m);
   var d = (end-start)/m;
   this.dataX = [];
   this.dataY = [];
   this.dataX[0] = start;   
   this.dataY[0] = f(start);   
   for (i=1;i<=m;i++) {
     this.dataX.push(start+i*d);   
     this.dataY.push(f(start+i*d));   
   }  
}

brd.createElement('text',[-6,-1,function(){ 
   var i,s,f0,f1;
   var m = n.Value();
   m = Math.floor(m);
   var d = (end-start)/m;
   s = 0.0;
   f0 = f(start);
   for (i=1;i<=m;i++) {
     f1 = f(start+i*d);
     s += Math.sqrt(d*d+(f1-f0)*(f1-f0));
     f0 = f1;
   }  
   return 'Length='+s.toFixed(4); }]);
</jsxgraph>