Distance as an Integral

    Notice that for we have which is the distance between and In fact, many quantities can be computed as the limit of a sum, not just area.

Proposition (Distance as an Integral) If an object has a position function and has continuous velocity function then total distance travelled by the object along a straight line from to is given by

    When the object moves forward (to the right) and when it moves backwards (to the left). In the general case, where changes sign n the time interval the integral measures the net distance or displacement of the object.

Example (Distance as an Integral) Find the total distance travelled by an object whose velocity function at time is on

    Solution.  

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