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Objectives

  • Explain the significance of the Net Change Theorem
  • Use the Net Change Theorem to solve applied problems

Summary

The net change theorem considers the integral of a rate of change. The net change theorem states that the integral of a rate of change will describe the net change between the given limits.

In essence, if we had a function describing the rate of change of a container filling up, C ′ ( x ) , with limits a and b describing time, then the amount of liquid put into the container between time a and time b can be found by doing the following ∫ a b C ′ ( x ) d x = C ( b ) − C ( a )

In the setting where we consider the integral of a velocity function  v ,  ∫ a b v ( t ) d t measures the exact change in position of the moving object on when [ a , b ]; when v is nonnegative,  ∫ a b v ( t ) d t is the object's distance traveled on [ a , b ].

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