Integral Help! Calculus

Question

The velocity function is v(t)=t^2-5t+4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-3,5].

Answer 1

Displacement is just the integral of v(t)dt from -3 to 5 in t.

Distance is positive definite. You have to separate the integral into regions of constant sign and add up the absolute values of the integral. You find the zeroes of v(t) --> t = 1, 4 by factoring

You can see that v is negative between these values so take the integral of vdt from -3 to 1 - integral from 1 to 4 + integral from 4 to 5.