Here, we can create various solids formed by stacking prisms (with varying cross-sectional bases parallel to the yAxis) from [i]x[/i] = a to [i]x[/i] = b. (Ex: see pic below). [br][br]We form such a solid by stacking prisms of width = dx & where [math]dx=\frac{b-a}{n}[/math]. [br]a = lower limit of integration (modifiable via slider)[br]b = upper limit of integration (also modifiable via slider)[br]n = number of prisms with height = dx. This is also modifiable by using the n slider. [br][br]You can also change [br]f(x) = upper (greater) function[br]g(x) = lower (lesser) function[br][br]For each of these demos (shown below), the upper function is [math]f\left(x\right)=-0.05x^2+12[/math], and the lower function is [math]g\left(x\right)=3\sin\left(x\right)-4[/math]. In these demos, a = -8 & b = 8. [br]

[b]Directions: [/b][br][br]1) Open up GeoGebra 3D app on your device. [br][br]2) Click on the 3 horizontal bars (upper left corner). Select [b]OPEN[/b]. [br][br]For cross sections parallel to the yAxis that are...[br][br][color=#38761d][b]EQUILATERAL TRIANGLES[/b] [/color](where f(x) - g(x) = one side), type this code: [b]XArpgR3A[/b][br][br][b]SQUARES [/b](where f(x) - g(x) = one side), type this code:[b] y7mnphxm[/b][br][br][b][color=#ff00ff]ISOSCELES RIGHT TRIANGLES[/color][/b] (where f(x) - g(x) = LEG), type this code: [b]shks2q7v[/b][br][br][b][color=#9900ff]REGULAR PENTAGONS[/color][/b] (where f(x) - g(x) = one side), type this code: [b]zmhqnrqb[/b][br][br][b][color=#0000ff]SEMICIRCLES[/color][/b] (with diameter = f(x) - g(x)), type this code: [b]cygnvepm[/b][br][br]