Math 125 – Week 3

Week 2 outline    Math 125 main page    Week 4 outline

What Where Link
Reading Text -- 6.1, 6.2, 6.3
Worksheet    Website – Area between curves AreaBetweenCurves.pdf
Worksheet 3 Solutions
Homework WebAssign WebAssign site for UW

Student Guide:

Moving on to Chapter 6, we learn some applications of integration. Here and throughout the quarter, it is important to understand how the formulas are derived. This helps you to learn how to apply integration to the problems you encounter in other fields.

We start with some general area problems in Section 6.1. Make sure you can do examples where the curves cross each other. In some examples, approximation techniques are necessary. You can use a Riemann Sum with midpoint sample points to get a good estimate.

Sections 6.2 and 6.3 cover methods of computing volumes. A general "slicing" method is introduced in section 6.2 -- as well as a subcategory of solids called solids of revolution. It is useful to practice visualizing these 3D solids. In section 6.2, the "slicing" method applied to solids of revolution is called "Disks/Wahers" (according to the shape of the cross-sections).

An alternative method of computing volumes of solids of revolution via "Shells" (empty cylinders) is discussed in section 6.3.

It's important to master and be able to apply all methods for computing volumes and to understand that, depending on the region to be rotated and on the axis of revolution, one of the methods may be much better than the other. That is, you should be able to determine when it's best to integrate with respect to x or y, and when to use shells or washers.

WORKSHEET: We can use integration to compute the area of a region that is bounded by curves. The examples given in the textbook are all fairly straightforward. The worksheet AreaBetweenCurves.pdf will guide you through the computation of the area of a more complicated region. It also explores the possible simplification of a problem by changing the integration variable.

Week 2 outline    Math 125 main page    Week 4 outline