gives you total displacement. gives you the total distance.
if i had a velocity function how would i find the displacement and distance traveled? the distance i'm guessing is an arclength but how do i find displacement? say and interval [-3,8].
I just made that equation up so I hope it works. but that means that I'd find the antiderivative of v(t), say V(t) is the antideriv, then find V(b)-V(a) and |V(b)-V(a)|. I'm really dumb when it comes to integrals.
and V(t) would be ? Isn't there a constant, c, I would then be missing?
distance and displacement are equal only if velocity is greater than or equal to 0 over the interval in question.
for your problem ...
this is why I broke up the integral into three pieces ... notice the middle integral has a negative sign before it in order to change the negative displacement over the interval to a positive value.
so ... total distance = [x(-1) - x(-3)] - [x(-1/2) - x(-1)] + [x(8) - x(-1/2)]