
UCD Mat 21B: Integral Calculus

5. Integration

• 5.1 Area and Estimating with Finite Sums
• 5.2 Sigma Notation and Limits of Finite Sums
• 5.3 The Definite Integral
• 5.4 The Fundamental Theorem of Calculus
• 5.5 Indefinite Integrals and the Substitution Rule
• 5.6 Substitution and Area Between Curves

6. Applications of Definite Integrals

• 6.1 Volumes Using Cross-Sections
• 6.2 Volumes Using Cylindrical Shells
• 6.3 Arc Length
• 6.4 Areas of Surfaces of Revolution
• 6.5 Work and Fluid Forces
• 6.6 Moments and Centers of Mass

7. Integrals and Transcendental Functions

• 7.1 The Logarithm Defined as an Integral
• 7.2 Exponential Change and Separable Differential Equations
• 7.3 Hyperbolic Functions
• 7.4 Relative Rates of Growth

8. Techniques of Integration

• 8.1 Integration by Parts
• 8.2 Trigonometric Integrals
• 8.3 Trigonometric Substitutions
• 8.4 Integration of Rational Functions by Partial Fractions
• 8.5 Integral Tables and Computer Algebra Systems
• 8.6 Numerical Integration
• 8.7 Improper Integrals

11. Parametric Equations and Polar Coordinates

• 11.1 Parametrizations of Plane Curves
• 11.2 Calculus with Parametric Curves
• 11.3 Polar Coordinates
• 11.4 Graphing in Polar Coordinates
• 11.5 Areas and Lengths in Polar Coordinates
• 11.6 Conic Sections
• 11.7 Conics in Polar Coordinates