An object moves along the x-axis with a velocity of v(t) = sin(pi/3)t for time t greater than or equal to 0. What is the total distance traveled by the object over the time interval 0 less than or equal to t less than or equal to 4?

Answer 1

well, from t = 0 to t = 3
sin(pi t/3 ) is positive

and
from t = 3 to t = 4, sin (pi t/3) is negative but the distance is still a positive quantity even if movingbackwards
so
integrate from t = 0 to t = 3
sin(pi t/3)dt
then integrate from t = 3 to t = 4
sin (pi t/3) dt
add the absolute values of both