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.
- 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.
- 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.
- 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.)
- To reposition the view, click and drag on the drawing pad and move it to the desired position.
- 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:
- 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]
- A full version of the GeoGebra software can be downloaded by following the link at the bottom of this page.