Find the average speed of a car, starting at time 0, if it drives for 5 hours and its speed at time t (in hours) is given by in miles per hour.
This problem is done just like any other average value problem. Integrating the speed function over the interval gives the total distance traveled since s'(t)=x(t). Dividing this by the length of the interval gives you the distance traveled in 1 hour, which gives you the average speed per hour. Thus the average speed is