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Shade region bounded by curves
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<iframe 
    src="https://www.jsxgraph.uni-bayreuth.de/share/iframe/shade-region-bounded-by-curves" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Shade region bounded by curves" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-1, 2, 2, -1],
        axis: true
    });
    
    // 1.  We need the mutual intersections of the curves.
    // However, only one intersection is not obvious.
    // Numerically compute intersection of the first two curves, '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. Plot curves only up to the mutual intersections
    // We use JessieCode for the function terms
    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. 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
        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();
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-1, 2, 2, -1],
    axis: true
});

// 1.  We need the mutual intersections of the curves.
// However, only one intersection is not obvious.
// Numerically compute intersection of the first two curves, '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. Plot curves only up to the mutual intersections
// We use JessieCode for the function terms
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. 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
    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 width="100%" aspect-ratio="1 / 1" title="Shade region bounded by curves" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-1, 2, 2, -1],
       axis: true
   });
   
   // 1.  We need the mutual intersections of the curves.
   // However, only one intersection is not obvious.
   // Numerically compute intersection of the first two curves, '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. Plot curves only up to the mutual intersections
   // We use JessieCode for the function terms
   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. 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
       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>

Shade region bounded by curves

Calculus
Curves
Function plotting
Somewhere in the world wide web the question was asked how to shade the region bounded by the following curves, where $x\ge 0$: $$ \begin{eqnarray*} x & \mapsto & \sqrt{x^2-1} \\ x & \mapsto & 0.707 x \\ x & \mapsto & 0 \\ \end{eqnarray*} $$ Here is a somewhat *hacky* the solution. The steps are: 1. First, we need the mutual intersections of the curves. However, only one intersection is not obvious. Numerically compute intersection of the first two curves, $\sqrt{x^2-1}$ and $0.707x$. 2. Plot curves only up to the mutual intersections. We use JessieCode for the function terms. 3. Plot a filled curve which linearly connects the points $(0,0)$, all points of the curve $\sqrt{x^2-1}$ and finally is closed by adding $(0,0)$ at the end. For other curves, especially, if the curves are closed, it might be easier to use the lement `CurveIntersection`.
// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-1, 2, 2, -1],
    axis: true
});

// 1.  We need the mutual intersections of the curves.
// However, only one intersection is not obvious.
// Numerically compute intersection of the first two curves, '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. Plot curves only up to the mutual intersections
// We use JessieCode for the function terms
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. 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
    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();

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.