What	Where	Link
Reading	Text – 6.1, 6.2 and 6.3
Worksheet	Website – Area between curves	AreaBetweenCurves.pdf
Homework	Website	week3probs.pdf Selected Answers

Student Guide:

Sections 6.2 and 6.3 cover volumes of solids of revolution. Many students have trouble visualizing these 3D solids. You should understand when to integrate with respect to x or y, and when to use shells or washers.

• We can use integration to compute the area of a region that is bounded by curves. The examples given in the textbook are all fairly straightforward. The worksheet AreaBetweenCurves.pdf will guide you through the computation of the area of a more complicated region. It also explores the possible simplification of a problem by changing the integration variable.
• The homework problems week3probs.pdf give examples of computing volumes. The first three problems are selections from the textbook.
• Problem 4 is sort of a real-world application of the techniques you use to compute volumes.
• Problem 5 shows you how you can generalize the methods of volume computation to more interesting shapes; at the same time, it tests your understanding of the concepts underlying volume integrals (i.e., the idea of adding "slices" to compute volumes).
• Problem 6 demonstrates how calculus can simplify problems in geometry (and how it can reveal the mysterious origins of volume formulas of solids).
• Problem 7 is a real-world application of both volume computation and integral approximation methods.