Math 125: Week 5
| Week 4 outline | Math 125 main page | Week 6 outline |
| What | Where | Link |
|---|---|---|
| Reading | Text - 6.4/6.5, 7.1, 7.2 | |
| Worksheet | Website – Integration by parts | IntByParts.pdf
Worksheet 5 Solutions |
Student Guide:
We start this week by continuing to discuss Work (sec 6.4) in additional situations, and developing one last application from Chapter 6, namely the Average Value of a Function, from section 6.5. You should try to get geometric insight into what this topic is about. Can you draw a picture that explains what the Average Value of a particular function is?
Chapter 7 is devoted to techniques for computing integrals. Some of these can be rather complex, and all of them require lots of practice to master.
- We start with Integration by Parts in Section 7.1. This is basically the Product Rule done backwards. Once you get the hang of it, you will probably not find it too difficult.
- The Trigonometric Integrals in Section 7.2 are useful on their own, but they are also needed to do Trigonometric Substitution in Section 7.3. Some of the integrals in Section 7.2 can get quite lengthy (and tricky, see Example 8!)
Worksheet: IntByParts.pdf explores the technique of Integration by Parts. It gives some ideas for choosing u and dv and shows how to use the technique to compute volumes. It also explores a common error in using the technique.
NOTE: You may find that you need to review some trigonometry, and completing the square, before studying Section 7.3 next week. Many students find this section difficult. Review these skills in advance!
| Week 4 outline | Math 125 main page | Week 6 outline |