Notes For Calc II (Topics) PDF

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summary of topics which sometimes is used in the exam and midterms for definitions...

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Notes For Calc II (Topics) part 2 Applications of Integrals - In this chapter we’ll take a look at a few applications of integrals. We will look at determining the arc length of a curve, the surface area of a solid of revolution, the center of mass of a region bounded by two curves, the hydrostatic force/pressure on a plate submerged in water and a quick look at computing the mean of a probability density function. The applications given here tend to result in integrals that are typically covered in a Calculus II course. 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 x or y 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....