Speedometer readings for a motorcycle at 12-seconds intervals are given in the table.

Question

t (sec) 0 12 24 36 48 60
v (ft/sec) 22 26 29 23 23 30

(a) Estimate the distance, in feet, traveled by the motorcycle during the time interval from 0 to 60 seconds using the velocities at the beginning of the time intervals.

(b) Give another estimate using the velocities at the end of the time periods.

Answer 1

(a) you want the Left Sum, so that is
12(f(0)+f(12)+f(24)+f(36)+f(48))
(b) the RS is just
12(f(12)+f(24)+f(36)+f(48)+f(60))