Accumulation

Part 5: Summary

1. If you have tabulated data on a rate-of-change function, how can you estimate the total change over an interval?
2. Under what circumstances does a left-hand sum overestimate an area under a curve? Under what circumstances does it underestimate the area?
3. Under what circumstances does a right-hand sum overestimate an area under a curve? Under what circumstances does it underestimate the area?
4. How can you improve on LHS and RHS as estimates of the area under a curve? Is this "improvement" always better than both LHS and RHS? Explain.