Upper and Lower Sums of a Curve
Questions to consider after typing a function into the input bar, choosing a start value from the start slider, and choosing an end value from the end slider:
1) How do the sums compare to the actual area under the curve when you use 3 rectangles? What about 20 rectangles? What about 100 rectangles?
2) If you were to assign one characteristic to the upper sum when comparing it to the actual area under the curve, what would it be? What about for the lower sum?
3) Do these characteristics still hold if you move the start and end values? Do the characteristics still hold if you changed the function?