MATH138 Lecture 3: Week 2 (Lecture 3-5) Lecture Notes

• School: University of Waterloo
• Department: Mathematics
• Course: MATH138
• Professor: Francis Poulin

Document Summary

Use integration by parts (recall ) (add on both sides) Example (could apply reduction formula or half angle formula) Math 138 page 1 (could apply reduction formula or half angle formula) (use double angle formula again) You expand the polynomial and then integrate each term. Power of is odd, then we separate one from the rest. If both are even, then use the half-angle identity. Case 1: if the power of the secant is even, (use trig identity) (polynomial that is easy to integrate) Case 2: if the power of tangent is odd, , then separate the integrand as follows: (use trig identity) Math 138 page 4 (polynomial that we can evaluate) Case 3: if the power of secant is odd and the power of tangent is even. Last trig integrals we consider are those that have different arguments. We established that the area of the ellipse is given by. The substitution we make is in a triangle.