Net Change Theorem and Applications of Integrals
In this video I go through what the net change theorem is and basically illustrate how this concept and the idea of integrals can be applied to any real world application that involves a known rate of change in which a net change is desired. Such an application involves filling a reservoir with water at a know rate and determining the net change in the reservoir volume. In the video I also go through an example explaining the difference between the displacement or net change of the position of a moving object with the total distance it travels.
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Applications of Integrals
The Net Change Theorem
This principle can be applied to all of the rates of changes in natural and social sciences.
Here are few examples:
Volume of water in a reservoir at time t:
Concentration of the product of chemical reaction at time t:
Mass of a rod of varying density
Rate of growth of a population n
Cost of producing x units
Position of an object moving in a straight line
Velocity change of the object: