### Accumulation

**Part 5: Summary**

- If you have tabulated data
on a rate-of-change function, how can you estimate the total change over
an interval?
- Under what circumstances
does a left-hand sum overestimate an area under a curve? Under what circumstances
does it underestimate the area?
- Under what circumstances
does a right-hand sum overestimate an area under a curve? Under what circumstances
does it underestimate the area?
- 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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authors <modules at math.duke.edu>
Last modified: November
18, 1997