Custom Surface of REV From 2 Functions (Calculus): Template
- Tim Brzezinski
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) To rotate the area between 2 function graphs about a HORIZONTAL AXIS (y = some number), type in the code BZWTCPfd. (It IS case sensitive). To rotate the area between 2 function graphs about a VERTICAL AXIS (x = some number), type in the code wendqwg7. (It IS case sensitive). 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!