calculus
posted by Anonymous .
The velocity function is v(t) =  t^2 + 4 t  3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [2,6].

displacement = integral v dt
= t^3/3 + 2 t^2  3 t
from 2 to +6
do the arithmetic
distance traveled
that means always use absolute value of any part of the integral
when is velocity negative and when is it positive?
0 = t^2  4 t + 3
0 = (t3)(t1)
velocity 0 at t = 1 and t = 3
so:
take absolute value of integral from
2 to + 1
add to absolute value of integral from +1 to +3
add to absolute value of integral from +3 to + 6 
thank you