Integral Calculus

Chapter 1: Introduction to Integrals

1.1: What are Integrals/Antiderivatives? Where do we use them? + Areas and Distances

1.2: Definite Integrals

1.3: Fundamental Theorem of Calculus

1.4: Indefinite Integrals and the Net Change Theorem + Substitution Rule

1.5: Approximate Integration and Midpoint Rule

Chapter 2: Applications of Integrals

2.1: Areas Between Curves

2.2: Volumes

2.3: Volumes By Cylindrical Shells

2.4: Work

2.5: Average Value of a Function

2.6: Arc Length

2.7: Area of a Surface of Revolution

2.8: Probability

Chapter 3: Techniques of Integration

3.1: Integration by Parts

3.2: U-Substitution

3.3: Trigonometric Integrals + Trigonometric Substitution

3.4: Integration of Rational Functions by Partial Fractions

3.5: Improper Integrals

3.6: Strategy for Integration

3.7: Integration Using Tables and Computer Algebra Systems

Chapter 4: Sequences and Series

4.1: Sequences

4.2: Series

4.3: Integral Test + Estimates of Sums

4.4: Comparison Tests

4.5: Alternating Series

4.6: Absolute Convergence and the Ratio and Root Tests

4.7: Power Series

4.8: Strategy for Testing Series + Representations of Functions as Power Series

4.9: Taylor and Maclaurin Series

Link to Textbook: Calculus Early Transcendentals, 8th Edition by James Stewart