Chapter 8. : Applications of Integrals

Here are a set of assignment problems for the Applications of Integrals chapter of the Calculus II notes. Please note that these problems do not have any solutions available. These are intended mostly for instructors who might want a set of problems to assign for turning in. Having solutions available (or even just final answers) would defeat the purpose the problems.

If you are looking for some practice problems (with solutions available) please check out the Practice Problems. There you will find a set of problems that should give you quite a bit practice.

Here is a list of all the sections for which assignment problems have been written as well as a brief description of the material covered in the notes for that particular section.

Arc Length – In this section we’ll determine the length of a curve over a given interval.

Surface Area – In this section we’ll determine the surface area of a solid of revolution, i.e. a solid obtained by rotating a region bounded by two curves about a vertical or horizontal axis.

Center of Mass – In this section we will determine the center of mass or centroid of a thin plate where the plate can be described as a region bounded by two curves (one of which may the \(x\) or \(y\)-axis).

Hydrostatic Pressure and Force – In this section we’ll determine the hydrostatic pressure and force on a vertical plate submerged in water. The plates used in the examples can all be described as regions bounded by one or more curves/lines.

Probability – Many quantities can be described with probability density functions. For example, the length of time a person waits in line at a checkout counter or the life span of a light bulb. None of these quantities are fixed values and will depend on a variety of factors. In this section we will look at probability density functions and computing the mean (think average wait in line or average life span of a light blub) of a probability density function.