Answer
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Work Step by Step
The Net Change Theorem, also known as the Fundamental Theorem of Calculus, states that if a quantity is changing over time and we know its rate of change, we can find the net change in the quantity over a certain interval by integrating its rate of change over that interval.
Specifically, regarding the integral of velocity, the Net Change Theorem implies that the integral of velocity over a given time interval gives the net displacement or change in position during that interval. In other words, if you integrate velocity with respect to time over a specific time interval, you'll find the total distance traveled by the object during that time.
Regarding the integral of marginal cost, the Net Change Theorem doesn't directly address marginal cost. However, in economics, the integral of marginal cost would represent the total cost incurred over a certain quantity produced. The connection lies in the fact that marginal cost represents the additional cost incurred by producing one more unit of a good, and integrating this over the quantity produced gives the total cost up to that quantity. So, the integral of marginal cost represents the total cost change associated with producing a certain quantity.
