What	Where	Link
Reading	Text – 7.1, 7.2 and 7.3
Worksheet	Website – Integration by parts	IntByParts.pdf
Homework	Website	week5probs.pdf Selected Answers

Student Guide:

The Trigonometric Integrals in Section 7.2 are needed to do Trigonometric Substitution in Section 7.3. Some of the integrals in Section 7.2 can get quite lengthy (and tricky, see Example 8). I've avoided the trickiest ones in the suggested homework.

You may find that you need to review some trigonometry, and completing the square, when studying Section 7.3. Many students find this section difficult.

• The 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.
• The first three homework problems in week5probs.pdf are selections from the textbook.
• Problem 4 requires you to compute the volume of a doughnut. Mmm, doughnut...
• Problem 5 can be seen as a sort of basic introduction to a more advanced mathematical topic, using only what you have learned so far about integration.
• Problem 6 is some practice in computing average values of functions. But you are also asked to interpret your answers geometrically – hence your understanding of this material must be deeper than just knowledge of the formulas involved.