The velocity in ft/s of an object moving along a line is given by v = 3t² + 1 on the interval 0 ≤ t ≤ 4.

a. Divide the interval [0, 4] into n = 4 subintervals, [0, 1], [1, 2], [2, 3], and [3, 4]. On each subinterval, assume the object moves at a constant velocity equal to v evaluated at the midpoint of the subinterval and use these approximations to estimate the displacement of the object on [0, 4] (see part (a) of the figure).

b. Repeat part (a) for n = 8 subintervals (see part (b) of the figure).

Transcribed Image Text:

v = 312 + 1 v = 3t2 + 1 50 40 40 30 20 10 10 2 3 2 3 4 (a) (b) 30 50 20