Quinn and Kelly are driving along a road and notice that the odometer has stopped working. They decide to try to determine the distance they have traveled by recording their velocity at certain times. The following table gives the velocities for the corresponding times from when they started recording.

Time, t (minutes)	0	2	4	5	6	9	12
Velocity,V (miles/hour)	48	50	52	55	58	60	65

1. Given velocity, write the limit notation for a right Riemann sum with n subintervals to find the distance traveled during the 12 minutes.

1. Write the integral that represents the distance traveled for these 12 minutes.

1. Rewrite the velocities so that the units are in miles/minute. Remember, 60 minutes = 1 hour.

Time,t(minutes)	0	2	4	5	6	9	12
Velocity,V (miles/minute)

1. From the data in the table, approximate the distance they traveled, using a left Riemann sum with 6 subintervals. All formulas and calculations must be shown.

1. Approximate the distance they traveled using a right Riemann sum with 6 subintervals. All formulas and calculations must be shown.

1. Is it appropriate to calculate the distance they traveled using a midpoint sum with 6 subintervals? Explain.

1. Approximate the distance they traveled using a midpoint sum with 3 subintervals. All formulas and calculations must be shown.

1. Approximate the distance they traveled using 6 trapezoids. All formulas and calculations must be shown.

1. Compare the distances you calculated. Which appears to give the best estimate of the distance they traveled, and why?