Math 125: Week 6

Week 5 outline    Math 125 main page    Week 7 outline

What Where Link
Reading Text - 7.2, 7.3, 7.4.
Worksheet    Website – Partial fractions PartialFractions.pdf
Worksheet 6 Solutions

Student Guide:

We're continuing to study methods of integration this week.

The Trigonometric Integrals in Section 7.2 are very useful on their own, but they are also 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).

We then cover 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.
  • The final integration technique we cover is Partial Fractions in Section 7.4. This is a fairly complex algebraic technique for simplifying rational functions. To make things 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 this section.
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