Strategy

In this chapter, we will be learning several techniques of integration. These techniques allow us to transform integrals into a form where we recognize the anti-derivative.

There are two components to this particular material.

1) Knowing the techniques

2) Knowing when to use them

As you work through each section, maintain a separate document where you record your thoughts on the features of the integral that coincided with the technique being studied. After all of the techniques have been covered, you should be able to construct a decision tree that guides you to the correct technique. 

Sections:

8.2: Integration by Parts

HW: 1 , 3 , 5 , 9 , 11 , 13 , 17 , 21 , 23 , 25 , 27 , 33 , 37 , 43 , 47 , 51 , 55 , 57 , 59 , 63 , 65

Board Problems: 3 , 5 , 9 , 11 , 13 , 21

Group Work: 25 , 27 , 57 , 63 , 65

Videos

8.3: Trigonometric Integrals

HW: 3 , 5 , 7 , 9 , 11 , 15 , 17 , 19 , 23 , 25 , 33 , 39 , 41 , 45 , 47 , 51 , 63 , 67 , 71

Board Problems: 11 , 15 , 17 , 25 , 41 , 47

Group Work: 71

Videos

8.4: Trigonometric Substitutions

HW: 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 23 , 31 , 53 , 55 , 58 , 62

Board Problems: 1 , 7 , 11

Group Work: 9 , 23 , 55 , 62

Videos

8.5: Integration of Rational Functions by Partial Fractions

HW: 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 33 , 37 , 57 , 61 , 63 , 73 , 77a

Board Problems: 11 , 17 , 21 , 33

Group Work: 73 , 77a

Videos

4.5: Indeterminant Forms and L'Hopital's Rule

HW: 3 , 13 , 15 , 19 , 23 , 27 , 29 , 31 , 35 , 41 , 49 , 51 , 53 , 59 , 63 , 65 , 67 , 79 , 85

Board Problems: 3 , 13 , 19 , 51

Group Work: 63 , 67 , 79

Videos

8.8: Part I: Evaluating Improper Integrals

HW: 1 , 3 , 5 , 11 , 13 , 19 , 23 , 25 , 29 , 33

Board Problems: 1 , 3 , 5

Group Work: 29 , 33

Videos