In this, the fifth and last section of the course, the topics include:
Applications of integrals.
• Appropriate integrals are used in a variety of applications to model physical,
biological, or economic situations. Although only a sampling of applications can be
included in any specific course, students should be able to adapt their knowledge
and techniques to solve other similar application problems. Whatever applications
are chosen, the emphasis is on using the method of setting up an approximating
Riemann sum and representing its limit as a definite integral. To provide a common
foundation, specific applications should include finding the area of a region, the
volume of a solid with known cross sections, the average value of a function, the
distance traveled by a particle along a line, and accumulated change from a
rate of change.
Applications of antidifferentiation
• Finding specific antiderivatives using initial conditions, including applications to
motion along a line.
• Solving separable differential equations and using them in modeling
(including the study of the equation y’ =?ky and exponential growth).