Math 125: Week 6

Week 5 outline    Math 125 main page    Week 7 outline

What Where Link
Reading Text - 7.3, 7.4
Worksheet    Website – Partial fractions PartialFractions.pdf
Worksheet 6 Solutions
Homework WebAssign
WebAssign site for UW

Student Guide:

We're continuing to study methods of integration this week. First we discuss the last two (and most complicated) techniques of integration:

  • Trigonometric Substitution in section 7.3 is about using reverse substitution and trigonometric identities to simplify certain integrals. Many students find this section difficult! If you haven't reviewed trigonometry and completing the square already, do so now.
  • Partial Fractions in section 7.4 is a fairly complex algebraic technique for simplifying rational functions. To make things a little easier, we cover only the cases where the denominator factors into linear terms, is itself an irreducible quadratic, or factors into (possibly repeated) linear terms times a single irreducible quadratic term. This should give you the basic idea of the technique. You'll probably have to review long division of polynomials.
  • The technique of Rationalizing Substitutions is also in section 7.4.

Finally, integrals requiring several techniques are presented in Section 7.5. These can be challenging, but also fun to puzzle out. This section does not cover any new material but it allows you to practice your integration skills and to develop better intuition for what methods to attempt. Doing lots of different integrals is essential to becoming proficient.

WORKSHEET: 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. This technique is also covered in lecture (section 7.4).

Week 5 outline    Math 125 main page    Week 7 outline