Riemann integrability: Difference between revisions

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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:[-3,4,3,-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',[-2.7,(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',[2.7,(Math.random()-0.5)*5]));
p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));


var f = brd.lagrangePolynomial(p);
var f = brd.lagrangePolynomial(p);
Line 12: Line 12:
var plot = brd.create('functiongraph',[f,-3,3]);
var plot = brd.create('functiongraph',[f,-3,3]);
   
   
var up = brd.createElement('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
var up = brd.create('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
var lo = brd.createElement('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});
var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});
   
   
/*
brd.createElement('text',[-2,-3,function(){ return 'Diff='+(brd.riemannsum(f,n.Value(),'upper',-3,3)-brd.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
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',[3,-3,'`sum_(i=0)^n i^2`']);
*/
</jsxgraph>
</jsxgraph>


[[Category:Calculus]]
[[Category:Calculus]]
[[Category:Examples]]
[[Category:Examples]]

Revision as of 12:44, 11 May 2010

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