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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.
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Last modified: November 18, 1997