Question: A tar engine leaves a station at time t = 0 driving east. The graph shows the velocity of the engine in miles per hour as a function of time in hours. Suppose the absolute area between the curve and the t-axis is: 1 on [0,1], 3 on [1,2], 5 on [2,3], and 7 on [3,4].

a) How far did the engine move in the easterly direction?

b) How far did the engine move in the westerly direction?

c) Evaluate \(\int\limits_{0}^{3}{v\left( t \right)dt}\)

d) Evaluate \(\int\limits_{0}^{4}{v\left( t \right)dt}\)

e) After four hours, where was the train relative to the station?