# Custom Surface of REV From 2 Functions (Calculus): Template

This applet dynamically illustrates the formation of a solid of revolution by rotating a region bounded by = upper function = lower function = lower limit of integration = upper limit of integration about ANY HORIZONTAL LINE (ranging from to ) or ANY VERTICAL LINE (ranging from to ). Simply input your upper function , your lower function , and your lower and upper limits of integration. Choose your options, and watch what happens. Note: You can also change a and b values by moving the pink and blue points (respectively) on the x-axis. You can also change the axis of rotation by moving the purple point on its respective axis. To explore in Augmented Reality, see the directions below this applet.

## TO EXPLORE IN AUGMENTED REALITY:

1) Open up GeoGebra 3D app on your device. 2) Click on the 3 horizontal bars (upper left). Select OPEN. 3) Type in the code BZWTCPfd. (It IS case sensitive). Note this string of characters = the last 8 digits of the URL for this resource. This graph defaults to rotating about a HORIZONTAL AXIS (y = some number) first. To rotate the area between 2 function graphs about a VERTICAL AXIS (x = some number), simply find the variable named m = false. Once you do so, change this line to m = true. To switch back to rotating about a HORIZONTAL AXIS, simply fine the line l = false. Change this line to l = true. 4) Once the resource loads, scroll upwards in the Algebra view (bottom) within this app. 5) The greater (higher) function is f (top most bar). You can modify this. The lesser (lower) function is h. You can modify this. a = lower limit of integration (modifiable) b = upper limit of integration (modifiable). n = the angle at which you will soon rotate this region (between the 2 graphs) about the line. c = the y-value of the horizontal line about which you will rotate (if you chose a horizontal axis). o = the y-value of the vertical line about which you will rotate (if you chose a vertical axis). s = the shading level of the surface (w/s = 0 being no shade and s = 1 = fully shaded). Leave the rest of the objects alone, and you'll be all set! Have fun exploring!