Dynamic Calculus

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Definite integral tool

The applet below is a simplified version of the GeoGebra software and may be used to sketch a variety of functions and to calculate the areas bounded by them. Instructions on how to draw the graph of a polynomial function and how to find the value of a related definite integral can be found at the bottom of this page.
[You can reset the applet at any time by clicking the 'circular arrows' icon in the top right corner]

 

 

To enter a function (for example \(f(x) = {x^2}\) use the following as a guide.

  1. In the 'input' field on the side of the applet, type:
    f=x
    then click the ⬚² button at the bottom of the page.
    (Alternatively, type f=x^2 then hit Enter).
    The equation \(f(x) = {x^2}\) should appear where you entered the function and the graph of the function should appear on the drawing pad.
  2. To change the equation of the function, click on the equation in the algebra window, make the desired changes and then hit Enter. The altered function will be drawn automatically.
  3. To zoom in, click the 'Zoom in' (+ magnifier) icon at the bottom of the applet.
    (To zoom out click the 'Zoom out' (- magnifier) icon and follow the same procedure.)
  4. To reposition the view, click and drag on the drawing pad and move it to the desired position.
  5. To calculate the area bounded by the curve, the \(x\)-axis and the ordinates \(x = 1\) and \(x = 3\), for example, enter the following command into the 'input' field at the bottom of the applet:
    Integral[f,1,3]
    (Alternatively, click on the f(x) tab, select ∫ and type f,1,3) The required area is displayed on the graph.

NOTES:

  1. More than one function may be entered onscreen by using different letters as 'names'. For example, the equation in (1) above could have been entered as:
    g=2x+1
    The derivative would then be found by entering the command:
    Integral[g,1,3]
  2. A full version of the GeoGebra software can be downloaded by following the link at the bottom of this page.