5.1 Integration & Anti-derivatives
Area Estimate Under a Function
Question #3 (Easy): Estimating the Total Amount Over the Time Interval
Any type of rate can be given over a time interval. But they can all be translated into the left and right
endpoint calculation for the lower and upper estimates for any total amount asked for over the interval.
Water is leaking from a swimming pool at the rates shown in the table at half-hour time interval.
1) Estimate the total amount of water leaked using the rates at the beginning of the time interval.
2) Estimate the total amount of water leaked using the rates at the end of the time interval.
3) Which estimates in parts a) and b) are the lower and upper estimates?
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
5.7 5.4 5.3 5.1 4.8 4.5 4.1 3.8 3.3
First, establish the input variables needed for summation regardless of the lower or upper estimates:
- In total 9 data points are give