Question

Speedometer readings for a vehicle (in motion) at 10-second intervals are given in the table.

t (sec) 0 10 20 30 40 50 60
v (ft/s) 0 9 33 59 75 72 53


Estimate the distance traveled by the vehicle during this 60-second period using the Riemann sums
L6:
R6:
M3:

Answer 1

To estimate the distance traveled by the vehicle during the 60-second period using Riemann sums, we can use three different methods: left endpoint approximation (L6), right endpoint approximation (R6), and midpoint approximation (M3).

Step-by-step explanation:

To estimate the distance traveled by the vehicle during the 60-second period using Riemann sums, we can use three different methods: left endpoint approximation (L6), right endpoint approximation (R6), and midpoint approximation (M3).

For L6, we sum the products of the width of each interval (10 seconds) and the height of the left endpoint of each interval. Summing the products gives us (10)(0) + (10)(9) + (10)(33) + (10)(59) + (10)(75) + (10)(72) = 2180 ft.

For R6, we sum the products of the width of each interval (10 seconds) and the height of the right endpoint of each interval. Summing the products gives us (10)(9) + (10)(33) + (10)(59) + (10)(75) + (10)(72) + (10)(53) = 2410 ft.

For M3, we sum the products of the width of each interval (10 seconds) and the height of the midpoint of each interval. Summing the products gives us (10)(4.5) + (10)(21) + (10)(46) + (10)(67) + (10)(73.5) + (10)(62.5) = 2280 ft.