During this weekend, you are to go for a 15-minute drive (preferably with a parent). You are to sit in the passenger's seat. Every minute, you should record the approximate speed of the car in miles per hour. Furthermore, you should record the exact mileage you traveled during that period of time (using the odometer). When you get home, graph your results (with the y axis as speed in mph and the x axis as each minute, or 1/60 of an hour). Your job: Use 15 rectangles with upper and lower sums to do two approximations of the area captured between your graph and the x-axis. These results should bound your actual mileage on the trip.

Tip: Measure the width of your rectangles in 1/60ths of an hour, not in minutes, so that your units are standard.

Difficulty Rating: 

You need to examine your speeds at the end of each one-minute interval. When doing upper sums, take the higher of the two as the height of the rectangle for that interval and vice versa for lower sums. Your upper and lower sums should contain the actual mileage.