探索积分
Task
Display the upper and lower sum of a function to explore the integral.
Explore the construction and learn how to create an applet for exploring the integral with GeoGebra Calculator Suite. Then try it yourself by following the instructions below.
Explore the construction...
Instructions
| 1. | | Enter the function into the Input Bar to draw its graph. |
| 2. |  | Create points A and B on the x-axis by selecting the Point tool and clicking on the x-axis. |
| 3. | | Enter the parameter into the Input Bar and press Enter. A slider for n will be created automatically. |
| 4. | | Open the context menu by pressing the More button of the slider and go to Settings to change the range from 1 to 50 and increment to 1. |
| 5. | | Enter the command to graph the upper sum in the Graphics View. |
| 6. | | Move the slider to change the number of intervals for the upper sum. |
| 7. | | Hide the upper sum by selecting the enabled Visibility button on the left in the Algebra View. |
| 8. | | Enter the command into the Input Bar to graph the lower sum. |
| 9. | | Move the slider again to change the number of intervals for the lower sum. |
| 10. | | Show the upper sum again, move the slider for the number of intervals and compare both values. Note: Change the colors of the upper and lower sum to compare them in the Graphics View. |
Try it yourself...
Instructions (continued)
| 11. | | Hide the lower and upper sum again by selecting the Visibility buttons. |
| 12. | | Enter the command to display the area between f(x) and the x-axis in this interval. |
| 13. | | Show the upper and lower sum again and move the slider. Note: Change the color of the integral to compare them in the Graphics View. |
| 14. | | Compare the values of the lower and upper sum with the integral when moving the slider to its maximum and explore how they get closer to the integral value. |