Upper and Lower Sums Applet
Directions: Use the applet below to explore the relationships between the upper and lower sums methods of finding the area under the curve. Also, compare to integration.
* Type in a function (in terms of x) into the opening.
*Drag points A and B along the x axis to change the starting and stopping points.
*Use the slider to change n, the number of rectangles.
*Check/Un-check boxes to show the upper sum, lower sum, and integral.
Consider the following questions as you explore:
1. Does the Upper Sum method over or under-estimate?
2. Does the Lower Sum method over or under-estimate?
3. Are there any relationships between the Upper and Lower Sum estimations and the actual area under the curve (integral?)