Math 125: Week 3
| Week 2 outline | Math 125 main page | Week 4 outline |
| What | Where | Link |
|---|---|---|
| Reading | Text - 5.5, 6.1, 6.2 | |
| Worksheet | Website – Area between curves | AreaBetweenCurves.pdf
Worksheet 3 Solutions |
Student Guide:
A lot of Math 125 is devoted to techniques for computing integrals. The first and most important technique, that of Substitution, in presented in Section 5.5. You should understand its relation to the Chain Rule. There are two methods for solving a Definite Integral using Substitution. You should be able to apply at least one of them correctly and consistently.
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. Two methods for computing volumes of solids of revolution are studied. In section 6.2, the "slicing" method for solids of revolution is called "Disks/Washers" (according to the shape of the cross-sections).
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 |