Mathematics

Calculus II

Integrals

  • Antiderivatives
  • Approximate Integration
  • Approximating Definite Integrals
  • Comparison Test for Improper Integrals
  • Computing Definite Integrals
  • Computing Indefinite Integrals
  • Constant of Integration
  • Definite Integral
  • Definition of the Definite Integral
  • Evaluating Definite Integrals
  • Improper Integrals
  • Improper Integrals
  • Indefinite Integrals
  • Integration by Parts
  • Integral and Comparison Tests
  • Integrals Involving Trig Functions
  • Integrals Involving Roots
  • Integrals Involving Quadratics
  • Integration of Exponential Functions
  • Integration by Parts
  • Integration by Parts
  • Integration of Rational Functions Resulting in Logarithmic or Arctangent Functions
  • Integration of Trigonometric Integrals
  • Integration Strategy
  • Method of Integration by Partial Fractions
  • Method of Integration by Power Substitution
  • Method of Trigonometric Substitution
  • Method of u-Substitution
  • Partial Fractions
  • Partial Fractions Integration
  • Substitution Rule
  • Substitution Rule for Definite Integrals
  • Substitution Rule for Indefinite Integrals, Part I
  • Substitution Rule for Indefinite Integrals, Part II
  • Trig Substitutions
  • Trigonometric Integrals and Substitutions
  • Top of Page
  • Integral Applications

  • Applications to Physics and Engineering
  • Arc Length
  • Arc Length
  • Areas Between Curves
  • Areas and Distances
  • Area Problems
  • Approximating Area Under a Curve with Rectangles
  • Area Between Two Curves
  • Area and Volume Formulas
  • Average Function Value
  • Center of Mass
  • Computing the Arc Length of a Differentiable Function on a Closed Interval
  • Computing the Areas of Enclosed Regions Using Vertical or Horizontal Cross-Sections
  • Hydrostatic Pressure and Force
  • Proof of Various Integral Properties
  • Surface Area
  • Volume Problems
  • Volumes of Solids of Revolution: Method of Cylinders
  • Volumes of Solids of Revolution: Method of Rings
  • Probability Using Integrals
  • Volumes
  • Volumes by Cylindrical Shells
  • Work
  • Top of Page
  • Parametric Equations

  • Arc Length with Parametric Equations
  • Arc Length with Polar Coordinates
  • Areas and Lengths in Polar Coordinates
  • Area with Parametric Equations
  • Area with Polar Coordinates
  • Calculus with Parametric Curves
  • Parametric Curves
  • Parametric Equations and Curves
  • Polar Coordinates
  • Polar Coordinates
  • Surface Area with Parametric Equations
  • Surface Area with Polar Coordinates
  • Tangents with Parametric Equations
  • Tangents with Polar Coordinates
  • Top of Page
  • Vectors

  • 3-D Coordinate System
  • Arc Length with Vector Functions
  • Basics of Vectors
  • Calculus with Vector Functions
  • Cross Product
  • Curvature
  • Cylindrical Coordinates
  • Dot Product
  • Equations of Lines in 3-D
  • Equations of Planes in 3-D
  • Functions of Several Variables
  • Quadratic Surfaces
  • Spherical Coordinates
  • Tangent, Normal, and Binormal Vectors
  • Vector Functions
  • Vector Arithmetic
  • Velocity and Acceleration
  • Top of Page
  • Resources

  • Calculus I Review and Practice Problems
  • Calculus II Review and Practice Problems
  • Calculus III Review and Practice Problems
  • Common Calculus Errors
  • MIT Open Courseware Calculus Textbook
  • Top of Page