Single Variable Calculus

4. Techniques of Integration

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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

Part C: Parametric Equations and Polar Coordinates

• Session 80: Parametric Curves
• Session 81: Examples Using Parametrized Curves
• Session 82: Polar Coordinates
• Session 83: Polar Coordinates, Continued
• Session 84: Polar Coordinates and Graphing
• Problem Set 11

Exam 4

• Session 85: Review for Exam 4
• Session 86: Materials for Exam 4

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