Table of Contents
xi
Chapter 14: Trigonometric Integrals, Trigonometric
Substitution, and Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
The Problems You’ll Work On ................................................................... 113
What to Watch Out For ............................................................................... 114
Trigonometric Integrals .............................................................................. 114
Trigonometric Substitutions ...................................................................... 116
Finding Partial Fraction Decompositions
(without Coefficients) .............................................................................. 117
Finding Partial Fraction Decompositions
(Including Coefficients) ........................................................................... 118
Integrals Involving Partial Fractions ......................................................... 118
Rationalizing Substitutions ........................................................................ 119
Chapter 15: Improper Integrals and More
Approximating Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
The Problems You’ll Work On ................................................................... 121
What to Watch Out For ............................................................................... 121
Convergent and Divergent Improper Integrals ........................................ 122
The Comparison Test for Integrals ........................................................... 123
The Trapezoid Rule ..................................................................................... 124
Simpson’s Rule ............................................................................................. 124
Part II: The Answers ................................................. 125
Chapter 16: Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . .127
Index ....................................................................... 595
xi
Chapter 14: Trigonometric Integrals, Trigonometric
Substitution, and Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
The Problems You’ll Work On ................................................................... 113
What to Watch Out For ............................................................................... 114
Trigonometric Integrals .............................................................................. 114
Trigonometric Substitutions ...................................................................... 116
Finding Partial Fraction Decompositions
(without Coefficients) .............................................................................. 117
Finding Partial Fraction Decompositions
(Including Coefficients) ........................................................................... 118
Integrals Involving Partial Fractions ......................................................... 118
Rationalizing Substitutions ........................................................................ 119
Chapter 15: Improper Integrals and More
Approximating Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
The Problems You’ll Work On ................................................................... 121
What to Watch Out For ............................................................................... 121
Convergent and Divergent Improper Integrals ........................................ 122
The Comparison Test for Integrals ........................................................... 123
The Trapezoid Rule ..................................................................................... 124
Simpson’s Rule ............................................................................................. 124
Part II: The Answers ................................................. 125
Chapter 16: Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . .127
Index ....................................................................... 595