Difference between revisions of "Shade region bounded by curves"

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Line 8: Line 8:
 
\end{eqnarray*}
 
\end{eqnarray*}
 
</math>
 
</math>
 +
 +
<jsxgraph width="600" height="400" box="box">
 +
const board = JXG.JSXGraph.initBoard('jxgbox', {
 +
    boundingbox: [-1, 3, 3, -1], axis:true
 +
});
 +
 +
// 1. step: compute intersection of 'sqrt(x^2-1)' and '0.707*x'
 +
var diff = x => Math.sqrt(x * x - 1) -  0.707 * x;
 +
var x_intersect = JXG.Math.Numerics.root(diff, 1.5);
 +
 +
// 2. step: plot curves only up to the mutual intersections
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// We use JessieCode for the function terms
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var curve1 = board.create('functiongraph', ['0', 0, 1]);
 +
var curve2 = board.create('functiongraph', ['sqrt(x^2-1)', 1, x_intersect]);
 +
var curve3 = board.create('functiongraph', ['0.707*x', 0, x_intersect]);
 +
 +
// 3. step: plot a filled curve which starts at (0,0), contains all points of 'sqrt(x^2-1)'
 +
// and is closed by adding (0,0) at the end.
 +
var curve = board.create('curve', [[], []], {strokeWidth:3, fillColor:'yellow', fillOpacity: 0.3});
 +
curve.updateDataArray = function() {
 +
  // Start with (0, 0)
 +
this.dataX = [0];
 +
  this.dataY = [0];
 +
 
 +
  // Copy all points from curve2
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  this.dataX = this.dataX.concat( curve2.points.map( p => p.usrCoords[1] ) );
 +
  this.dataY = this.dataY.concat( curve2.points.map( p => p.usrCoords[2] ) );
 +
 
 +
  // Close the curve by adding (0,0)
 +
  this.dataX.push(0);
 +
  this.dataY.push(0);
 +
};
 +
board.update();
 +
</jsxgraph>

Revision as of 16:03, 18 June 2020

Somewhere in the WWW the question was asked how to shade the region bounded by the following curves, where [math]x\ge 0[/math]:

[math] \begin{eqnarray*} x & \mapsto & \sqrt{x^2-1} \\ x & \mapsto & 0.707 x \\ x & \mapsto & 0 \\ \end{eqnarray*} [/math]