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

Question

t (sec) 0 10 20 30 40 50 60

v (ft/s) 0 10 35 62 79 76 56

Estimate the distance traveled by the vehicle during this 60-second period using L6, R6 and M3.

Answer 1

s(t) = ∫v(t)dt

Estimate with Riemann sums

Δx = (60-0)/6 = 10

L6: ∑f(x_i-1)Δx

10[0+10+35+62+79+76] = 10(262) = 2620 ft

R6: ∑f(x_i)Δx

10[10+35+62+79+76+56] = 10(318) = 3180 ft

M3: ∑f((x_i-1+x_i+1)/2))Δx Δx = (60-0)/3 = 20

20[f(10)+f(30)+f(50)] = 20[10+62+76] = 20(148) = 2960 ft