Use the trapzoid rule to estimate the distance traveled by the car during the 12 seconds

Question

A car going 88 ft/sec brakes to a stop in 12 seconds. The velocity is recorded every 3 seconds and is given in the table below. Use the trapezoidal rule to estimate the distance traveled by the car during the 12 seconds

Values: (0,88) (3,54) (6,36) (9,12) (12,0)

Answer 1

The distance traveled will be the Area under the curve defined by the sample points.

distance = A_T = (Δx/2)(f(0) + 2(f(3) + 2f(6) + 2f(9) + f(12))

Δx = 3

distance = (3/2)(88 + 2(54) + 2(36) + 2(12) + 0)

=(3/2) (88 + 108 + 72 + 24)

= (3/2)(292)

= 438 feet