Now let's switch gears and think back to the Fundamental Theorem of Calculus.  If we replace the integrand with a rate of change of some quantity, say water in a pipe, we can interpret the answer as a net change in the amount of that quantity.  Duration: 3:30

Using a definite integral of the rate at which water flows into a drainpipe (who measures such a thing?), we arrive at the total amount of water the pipe experienced over some time interval.  Perhaps an examination of the units involved in the problem will help you understand the process here.  Duration: 13:57

Next up, we have displacement, or the net change in the distance traveled by an object undergoing rectilinear motion.  Duration: 10:17

In Example 9, we're tasked with finding the absolute maximum velocity given the graph of the acceleration function.  Solving this FRQ will require the use of the Closed Interval Test on an integral equation.  Duration: 13:32

If we wanted to find the total distance traveled by an object, we must integrate the speed function.  Example 10 demonstrates this tedious technique.  Duration: 8:10evaluating definite integrals a breeze, but what are you supposed to do when you can't find an antiderivative?  Example 11 presents such a case, and don't worry, we still don't have to revert back to a the limit of a Riemann sum.  Duration:7:22

This final example is a free-response extension to the previous exercise.  While the first part of the question has little to do with the current lesson, it is a welcome review of an older concept.  Duration: 4:16