Question

A particle moves in a straight line with velocity 9−12𝑡+3𝑡^2 ft/s. Find the total total distance traveled over the time interval [1,6]

Answer 1

integral from t = 1 to t = 6
9 t - 6 t^2 + t^3 at t = 6 - at t = 1
at 6
9*6 - 6^3 + 6^3 = 54 (convenient)
at 1
9 - 6 + 1 = 4
54 - 4 = 50 feet