- Some: #2, p. 235
- others: f(x)=1/x-7
- Dirt!
- Suppose that you clock your speed at each minute along a trip, in
mph:
Estimate the distance travelled.minute 0 1 2 3 4 5 6 7 8 9 10 speed (mph) 0 30 45 30 70 65 70 70 45 30 35
- Suppose that you clock your speed at each minute along a trip, in
mph:
- Trapezoidal rule
- Assumes continuity of underlying speed function
- We fit straight line segments between data points
- Left/Right/Midpoint rules
- relax continuity! Use rectangles...
- also called rectangle rules: lrr, rrr
- Basically, every function can be used to create a table like this, and
then we can use these strategies.
- Here's an important theorem:
- Examples:
- #5, p. 258 (also trapezoidal)
- #9, p. 258