5.1 Integration & Anti-derivatives
Area Estimate Under a Function
Question #2 (Easy): Calculating the Total Distance
These word questions will provide a table of values for time and velocity, then ask to:
- Find the lower estimate and upper estimates of the total distance travelled.
o This equates to the total area under the curve.
When the question says use the rates at the beginning of the time interval, it means use the left
Likewise, using the rates at the end of the time interval means use the right endpoints.
Matching which one is the lower estimate and the upper estimate is based on the calculated values
- Smaller estimate = lower estimate; Greater estimate = upper estimate
Another way to spot is to see if the velocity is consistently increasing or decreasing over the time
- If increasing: left endpoints = lower estimate; right endpoints = upper estimate
- If decreasing: left endpoints = upper estimate; right endpoints = lower estimate
A jogger runs at a steadily increasing speed in the first 60 seconds of his exercise.
His speed at 10-second interval is given in the table below.
Find the lower estimate an