Difference between revisions of "Riemann integrability"

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(New page: <jsxgraph width="800" height="400" box="box"> var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true}); var p = []; p.push(brd.create('point',[-2,(Math.random()-0.5)*5]...)
 
 
(8 intermediate revisions by one other user not shown)
Line 1: Line 1:
 
<jsxgraph width="800" height="400" box="box">
 
<jsxgraph width="800" height="400" box="box">
var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true});
+
var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,5,3,-3],axis:true});
 
var p = [];
 
var p = [];
p.push(brd.create('point',[-2,(Math.random()-0.5)*5]);
+
p.push(brd.create('point',[-2.7,(Math.random()-0.2)*5]));
p.push(brd.create('point',[-1,(Math.random()-0.5)*5]);
+
p.push(brd.create('point',[-1,(Math.random()-0.2)*5]));
p.push(brd.create('point',[0,(Math.random()-0.5)*5]);
+
p.push(brd.create('point',[0,(Math.random()-0.2)*5]));
p.push(brd.create('point',[1,(Math.random()-0.5)*5]);
+
p.push(brd.create('point',[1,(Math.random()-0.2)*5]));
p.push(brd.create('point',[2,(Math.random()-0.5)*5]);
+
p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));
  
var f = brd.lagrangePolynomial(p);
+
var f = JXG.Math.Numerics.lagrangePolynomial(p);
 
var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
 
var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
 
var plot = brd.create('functiongraph',[f,-3,3]);
 
var plot = brd.create('functiongraph',[f,-3,3]);
 
   
 
   
/*
+
var up = brd.create('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
var os = brd.createElement('riemannsum',[f,  
+
var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});
    function(){ return s.Value();}, function(){ return document.getElementById('sumtype').value;},
 
    function(){return a.Value();},  
 
    function(){return b.Value();}
 
    ],  
 
    {fillColor:'#ffff00', fillOpacity:0.3});
 
 
   
 
   
brd.createElement('text',[-6,-3,function(){ return 'Sum='+(brd.riemannsum(f,s.Value(),document.getElementById('sumtype').value,a.Value(),b.Value())).toFixed(4); }]);
+
brd.create('text',[-2,-2,function(){ return 'Diff='+(JXG.Math.Numerics.riemannsum(f,n.Value(),'upper',-3,3)-JXG.Math.Numerics.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
 +
</jsxgraph>
 +
 
 +
===The underlying JavaScript code===
 +
<source lang="javascript">
 +
var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,5,3,-3],axis:true});
 +
var p = [];
 +
p.push(brd.create('point',[-2.7,(Math.random()-0.2)*5]));
 +
p.push(brd.create('point',[-1,(Math.random()-0.2)*5]));
 +
p.push(brd.create('point',[0,(Math.random()-0.2)*5]));
 +
p.push(brd.create('point',[1,(Math.random()-0.2)*5]));
 +
p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));
 +
 
 +
var f = JXG.Math.Numerics.lagrangePolynomial(p);
 +
var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
 +
var plot = brd.create('functiongraph',[f,-3,3]);
 +
 +
var up = brd.create('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
 +
var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});
 
   
 
   
brd.create('text',[3,-3,'`sum_(i=0)^n i^2`']);
+
brd.create('text',[-2,-2,function(){ return 'Diff='+(JXG.Math.Numerics.riemannsum(f,n.Value(),'upper',-3,3)-JXG.Math.Numerics.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
*/
+
</source>
</jsxgraph>
 
  
 
[[Category:Calculus]]
 
[[Category:Calculus]]
 
[[Category:Examples]]
 
[[Category:Examples]]

Latest revision as of 21:09, 18 January 2013

The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,5,3,-3],axis:true});
var p = [];
p.push(brd.create('point',[-2.7,(Math.random()-0.2)*5]));
p.push(brd.create('point',[-1,(Math.random()-0.2)*5]));
p.push(brd.create('point',[0,(Math.random()-0.2)*5]));
p.push(brd.create('point',[1,(Math.random()-0.2)*5]));
p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));

var f = JXG.Math.Numerics.lagrangePolynomial(p);
var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
var plot = brd.create('functiongraph',[f,-3,3]);
 
var up = brd.create('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});
 
brd.create('text',[-2,-2,function(){ return 'Diff='+(JXG.Math.Numerics.riemannsum(f,n.Value(),'upper',-3,3)-JXG.Math.Numerics.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);