INTEGRALS
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INTEGRALS
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1. Antiderivative and Indefinite Integral
Theory
Page 10
1A. Definition of the Indefinite Integral
Theory
Page 10
1B. Properties of the Indefinite Integral
Theory
Page 12
1C. Basic Integration Formulas
Theory
Page 14
Exercises 1.1
Problem
Page 24
2. Integration Methods
Theory
Page 26
2A. Integration by Substitution
Theory
Page 26
2B. Integration by Parts
Theory
Page 33
2C. Integrating Partial Fractions
Theory
Page 38
2D. Integrating Radical Fractions
Theory
Page 45
2E. Integrating Trigonometric Functions
Theory
Page 49
Exercises 1.2
Problem
Page 55
Chapter Summary
Theory
Page 57
Concept Check
Test
Page 58
Chapter Review Test 1A
Test
Page 59
Chapter Review Test 1B
Test
Page 61
Chapter Review Test 1C
Test
Page 63
1. Evaluating Definite Integrals
Theory
Page 66
1A. Definition of the Definite Integral
Theory
Page 66
1B. The Fundamental Theorem of Calculus
Theory
Page 68
1C. Properties of the Definite Integral
Theory
Page 69
1D. Leibniz’s Rule
Theory
Page 74
1E. The Mean Value Theorem
Theory
Page 75
Exercises 2.1
Problem
Page 76
2. Integrals of Some Special Functions (Optional)
Theory
Page 77
2A. Integrating Absolute Value Functions
Theory
Page 77
2B. Integrating Sign Functions
Theory
Page 79
2C. Integrating Floor Functions
Theory
Page 80
Exercises 2.2
Problem
Page 83
Chapter Summary
Theory
Page 84
Concept Check
Test
Page 84
Chapter Review Test 2A
Test
Page 85
Chapter Review Test 2B
Test
Page 87
1. Finding the Area Under a Curve
Theory
Page 90
Exercises 3.1
Problem
Page 97
2. Other Applications
Theory
Page 100
2A. Calculating the Volume of a Solid of Revolution
Theory
Page 100
2B. Finding the Length of a Curve (Optional)
Theory
Page 104
2C. Calculating the Area of a Surface of Revolution (Optional)
Theory
Page 105
Exercises 3.2
Problem
Page 107
Chapter Summary
Theory
Page 109
Concept Check
Test
Page 109
Chapter Review Test 3A
Test
Page 110
Chapter Review Test 3B
Test
Page 112
Answers
Answer
Page 114
Glossary
Other
Page 118
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