Question

Find the distance traveled by an object on the interval [0, 5] if its velocity is v(t)= sin(pi/3t)

Answer 1

distance is defined by:
d = \[\int\limits_{a}^{b} | v(t) |\ dt\]

Answer 2

So in your case it would be
\[\int\limits\limits_{0}^{5} | \sin(\frac{\pi}{3}t) |\ dt\]

= 21/(2pi)