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Mathematics LibreTexts

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