Upper and Lower Sums
This applet will allow you to investigate the lower and upper sums of the area under a curve. You can change the function by entering the function of your choice into the box that says function Then you have the choice to move the slider a (upper sum) and slider b (lower sum) to move the upper and lower ranges. The n slider changes the number of rectangles under the curve. Lastly, by checking/unchecking the checkboxes, you may choose to look at only the upper sum, lower sum, or integral sum.
Things to think about:
1. What is the relationship between the curve and the Upper sum? Lower sum?
2. Observe the Upper and Lower sums how do they relate to the integral? Make a conjecture about the relationship between the Upper and lower sums and the integral.
3. Look at the Upper and Lower Sums investigate by moving the a, b, and n slider. What happens when b=-a? Why does this happen?