Chapter 5.1, Problem 6E

The velocity in ft/s of an object moving along a line is given by v – f(t) on the interval 0 < t < 10 (see figure), where t is measured in seconds.

  a.    Divide the interval [0, 10] into n – 5 subintervals. On each subinterval, assume the object moves at a constant velocity equal to the value of v evaluated at the left endpoint of the subinterval, and use these approximations to estimate the displacement of the object on [0, 10].

  b.    Repeat part (a) using the right endpoints to estimate the displacement on [0, 10].

  c.    Repeat part (a) using the midpoints of each subinterval to estimate the displacement on [0, 10].