The velocity of an object is given by v(t)=t(t^2-1)^(1/3) feet per second. Find the total number of feet traveled by the object in the time interval [0,3] seconds.
(A)51/4
(B)34/3
(C)45/4
(D)51/8
(E)45/8
let z = t^2-1
then dz = 2 t dt or dt =dz/(2 t)
and we have
integral of
t z^(1/3) dt = t z^(1/3) dz/(2t)
= (1/2) z^(1/3) dz
Got it :)