Difference between revisions of "Riemann integrability"
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<jsxgraph width="800" height="400" box="box"> | <jsxgraph width="800" height="400" box="box"> | ||
| − | var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3, | + | 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. | + | p.push(brd.create('point',[-2.7,(Math.random()-0.2)*5])); |
| − | p.push(brd.create('point',[-1,(Math.random()-0. | + | p.push(brd.create('point',[-1,(Math.random()-0.2)*5])); |
| − | p.push(brd.create('point',[0,(Math.random()-0. | + | p.push(brd.create('point',[0,(Math.random()-0.2)*5])); |
| − | p.push(brd.create('point',[1,(Math.random()-0. | + | p.push(brd.create('point',[1,(Math.random()-0.2)*5])); |
| − | p.push(brd.create('point',[2,(Math.random()-0. | + | p.push(brd.create('point',[2.7,(Math.random()-0.2)*5])); |
| − | var f = | + | 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 | + | 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); }]); | |
| − | brd. | ||
| − | |||
| − | |||
</jsxgraph> | </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',[-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> | ||
[[Category:Calculus]] | [[Category:Calculus]] | ||
[[Category:Examples]] | [[Category:Examples]] | ||
Latest revision as of 20:09, 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); }]);
