Math 125: Week 7
| Week 6 outline | Math 125 main page | Week 8 outline |
| What | Where | Link |
|---|---|---|
| Reading | Text – 7.7, 7.8, 8.1 | |
| Worksheet | Website – Techniques of Integration | IntegrationTechniques.pdf
Worksheet 7 Solutions |
| Homework | WebAssign |
WebAssign site for UW
|
Student Guide:
We have already seen how to approximate integrals using Riemann Sums. This works quite well if we use midpoints for our sample points. Section 7.7 introduces two more techniques for approximating integrals that you just can't compute, the Trapezoid Rule and Simpson's Rule. These are key techniques for use in applications. Most instructors skip the error estimation formulas. They are mostly of theoretical interest. In practical applications, the error of your approximation is estimated using other methods.
Improper Integrals are covered in Section 7.8. These are a combination of a Definite Integral and a Limit. There are two types of Improper Integral and you should understand the difference. You should understand convergence and divergence. You'll probably have to review limits in general, and particularly one-sided limits when studying integrals that are improper because of discontinuity. L'Hospital's Rule is also useful here. Note that to earn full credit on an improper definite integral exam question you will need to be able to set it up correctly as a limit, and compute the resulting limit.
We return to a couple more applications of integrals in Chapter 8. As before, the method of going from a problem to an integral is more important than any particular formulas we cook up. We study how to compute the length of a curve in Section 8.1. You should understand the derivation of the formula. It is often very difficult to compute the integrals that come up in this section. This is a good place to apply approximation techniques.
WORKSHEET: We have now learned several techniques for computing integrals. Integrals that are encountered in real applications often require more than one technique to solve them. These problems can be quite challenging. The worksheet IntegrationTechniques.pdf gives several examples of this type of integral. You are encouraged to ask the TA for help if you get stuck!
| Week 6 outline | Math 125 main page | Week 8 outline |