A car moves along a straight road in such a way that its velocity (in feet per second) at any time t (in seconds) is given by

Question

v(t) = 3t sqrt(64−t^2)
(0 ≤ t ≤ 8).
Find the distance traveled by the car in the 8 sec from t = 0 to t = 8.

Answer 1

distance is

∫[0,8] 3t√(640t^2) dt
= 512