This resource can be used to illustrate how a solid of revolution is formed by rotating the area bound by the yAxis, a function [i]f[/i], and the vertical lines [i]x = a[/i] & [i]x = b[/i]. [br][br]When a differential rectangle is spun around the xAxis, it creates a surface of revolution called a [i]disc[/i]. [br][b][br]You can alter the following parameters:[/b][br][br]function [i]f[br][/i]lower limit of integration ([i]a[/i])[br]upper limit of integration ([i]b[/i])[br]n = number of differential rectangles. [br][br]The width of each rectangle = [math]\Delta x=\frac{b-a}{n}[/math][br][br][b][color=#1e84cc]To explore this resource in Augmented Reality, see the directions below the first screencast. [/color][/b]
Given that the width of each differential rectangle = [math]\Delta x[/math] and the height of each rectangle = [math]f\left(x\right)[/math], write an expression for the volume of one disc.
1) Open up GeoGebra 3D app on your device. [br] [br]2) Go to the menu (upper left). Select OPEN. Under SEARCH, type [b]s7mqyzee[br][br][/b]3) The [math]\alpha[/math] slider controls the angle. [br] [b]a [/b]and [b]b [/b]control the upper and lower limits of integration. [br] The colored filling sliders are also there. [br] To change the function (even though it's labeled "[b]f[/b]"), change function [b]h[/b]. [br] [b]n = number of discs[/b].