### Introduction

This unit covers advanced integration techniques, methods for calculating the length of a curved line or the area of a curved surface, and “polar coordinates” which are an alternative to the Cartesian coordinates most often used to describe positions in the plane.

**Part A: Trigonometric Powers, Trigonometric Substitution and Completing the Square**

- Session 68: Integral of sinn(x) cosm(x), Odd Exponents
- Session 69: Integral of sinn(x) cosm(x), Even Exponents
- Session 70: Preview of Trig Substitution and Polar Coordinates
- Session 71: Integrals Involving secant, cosecant and cotangent
- Session 72: Trig Substitution
- Session 73: Completing the Square
- Problem Set 9

**Part B: Partial Fractions, Integration by Parts, Arc Length, and Surface Area**

- Session 74: Integration by Partial Fractions
- Session 75: Advanced Partial Fractions
- Session 76: Integration by Parts
- Session 77: Volume of a Wine Glass
- Session 78: Computing the Length of a Curve
- Session 79: Surface Area
- Problem Set 10