This applet dynamically illustrates how rotating an [b]arc length[/b] of a piece of the graph of a function [math]f[/math] , from [math]x=a[/math] to [math]x=b[/math], about an axis, generates a [b][color=#a64d79]surface of revolution[/color][/b]. [br][br]For simplicity, the axis of revolution here is the [i]x[/i]-axis. [br][br]You can alter the values of [br][br][math]a[/math] = lower limit of integration[br][math]b[/math] = upper limit of integration[br][math]n[/math] = number of equal intervals into which the interval [math]\left[a,b\right][/math] is divided. [br][br]How does increasing the value of [math]n[/math] change the appearance of the [b][color=#a64d79]surface of revolution[/color][/b]? [br][br][color=#1e84cc][b]To explore this in Augmented Reality, see directions below this interactive figure. [/b][/color]

1) Open up GeoGebra 3D app on your device. [br]2) Select the MENU (3 horizontal bars upper left). [br]3) Select [b]OPEN[/b]. Under "Search", type [b]dbska9aq[br][/b]4) Select the 1 option that appears. [br][br]5) You can alter function [b]f[/b], lower limit of integration [b]a[/b], upper limit of integration [b]b[/b], and [b]n [/b]= number of [br] intervals where each [math]dx=\frac{b-a}{n}[/math].