What	Where	Link
Reading	Text – 7.8 and 8.1
Worksheet	Website – Techniques of Integration	IntegrationTechniques.pdf
Homework	Website	week7probs.pdf Selected Answers

Student Guide:

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 one-sided limits when studying integrals that are improper because of discontinuity. L'Hospital's Rule is also useful here.

We cover a few more applications 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.

• 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!
• You will find some challenging integration problems in week7probs.pdf. The first two problems are selections from the textbook.
• Problem 3 shows how to use integral approximation techniques to estimate the arc length of a curve. Computing an arc length integral is often rather nasty, if not impossible, so approximation can be necessary.
• Problem 4 presents a classic arc length problem, computing the arc length of a cycloid. Have you ever wondered how far a stone stuck in a car tire actually travels? Now you'll know.
• Problem 5 is the sequel to Problem 3 of Week 4 – now you compute the work done in blasting a rocket into space from the surface of the moon.