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 | |
| Worksheet | Website – Integration by parts | IntByParts.pdf
Worksheet 5 Solutions |
Student Guide:
Another application of integrals we study is computing the Work required to perform certain more complicated tasks. While the concept of Work is important in Physics, the main Calculus concept to get here is another example of taking a problem and turning it into an integral. It is essential to understand the process of behind setting up the integrals. Practice setting up each problem carefully and do not skip steps.
The last application we study in Chapter 6 is in section 6.5, Average Value of a Function. 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 challenging.
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.
- 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 |