# Math Help - Integral Application

1. ## Integral Application

A particle moves in a straight line with velocity ft/s. Find the total displacement and total distance traveled over the time interval .

I found that the displacement was 0.661458 ft., but I cannot find the total distance. I don't think my displacement is right, please help!

2. Well, remember that $\frac{dx}{dt}=v$

Thus we have: $\int_{t_1}^{t_2} v \cdot{dt}=x(t_2)-x(t_1)=\Delta x$

(Fundamental Theorem)

Where $x(t)$ is the position at the time t

With that you get the distance traveled