Approximating the area under a curve
This applet allows you to investigate upper and lower sums as a method for finding the area under a curve.
Exploration Instructions
1. Enter an interesting function
2. Make a rough prediction about the what the area under the curve is
3. Set the number of rectangles = 1
4. Show the upper sum
5. Slowly increase the number of rectangles. How does the sum change?
6. Hide upper sum
7. Set the number of rectangles = 1
8. Show the lower sum
9. Slowly increase the number of rectangles. How does the sum change?
10. Show both the upper and lower sum. How do the sums change in comparison to each other?
11. The upper and lower sum provide an interval in which the true area under the curve is
12. Show the integral.
13. Describe the similarities and differences between upper sum, lower sum, and integral.