Determine the distance traveled from the following velocity data:
t 1 2 3.25 4.5 6 7 8 8.5 9 10
v 5 6 5.5 7 8.5 8 6 7 7 5
(a) Use the trapezoidal rule. In addition, determine the average velocity.
(b) Fit the data with a cubic equation using polynomial regression. Integrate the cubic equation to determine the distance.