What	Where	Link
Reading	Text – 7.4, 7.5 and 7.7
Worksheet	Website – Partial fractions	PartialFractions.pdf
Homework	Website	week6probs.pdf Selected Answers

Student Guide:

Integrals requiring several techniques are presented in Section 7.5. These can get rather difficult. The homework focuses on the more straight-forward examples.

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.

• The technique of Partial Fractions is not really calculus. It is just some fairly complicated algebra. However, most students have difficulty with algebra. The worksheet PartialFractions.pdf will guide you through the nuts and bolts of the technique.
• The supplementary homework problems can be found here: week6probs.pdf. The first three problems are selections from the textbook.
• Problem 4 combines approximation techniques with volume computation techniques. Exam writers love to force you to use multiple concepts in one problem.
• Problem 5 is a long list of integrals that have appeared on exams in the past. You can expect similar integrals to appear on future exams.
• Problem 6 is meant to give you practice in looking at a problem and determining which technique of integration you should use.
• Note that Problem 7 is optional. It is included to help you study. You do not need to hand it in (unless your professor tells you to).