Upper and Lower Sums
Compare the Upper and Lower Sums
1. Type in a function to explore.
2. Choose boundaries on the x-axis by dragging the two points.
3. Drag the slider to choose a number of rectangles for your lower and upper sum approximations.
4. Click the Show Upper Sum to view the Upper Sum rectangles and their total signed area.
5. Click the Show Lower Sum to view the Lower Sum rectangles and their total signed area.
6. Try changing the number of rectangles. How do the Upper and Lower Sums change as n changes?
7. Click Show Integral to see the exact value of the signed area under he curve between your two points.