Course curriculum

  • 1
    Welcome to the Course!
    • Download the Integration Cheat Sheet Here
  • 2
    Type 1: Anti-Derivatives
    • Integration is the Reverse Process of Differentiation
    • Integration of Polynomials
    • The Most Important Integrations to Memorize
    • Two Challenging Problems
    • Test Your Learning
  • 3
    Type 2: u-Substitution
    • The 3 Easy Steps for u-Substitution
    • Two Solved Examples
    • The 4 important types of u-Substitution problems
    • Test Your Learning
  • 4
    Type 3: Area Under a Curve
    • The 2 steps in Evaluating Definite Integrals
    • Integration is just the Area under a Curve
    • Simplifying complicated Integrations with Geometry
    • Two Solved Examples
    • Test Your Learning
  • 5
    Type 4: Riemann Sums
    • Approximating Areas using Rectangles
    • Left and Right Endpoint Methods
    • The Trapezoidal Method
    • Test Your Learning
  • 6
    Type 5: Area Enclosed between Two Curves
    • The Formula to calculate Area between Curves
    • Solved Example: Area Enclosed between Two Parabolas
    • Integrating Along the Y Axis
    • Integrating Along the Y Axis to Find Enclosed Areas
    • Test Your Learning
  • 7
    Type 6: Volumes - Using Disks & Washers
    • Using Disks to Calculate Volumes
    • Using Washers to Calculate Volumes of Hollow Solids
    • Rotation Around the Y Axis
    • Test Your Learning
  • 8
    Type 7: Volumes - Using Cross-Sections
    • Calculating Volumes using Thin Cross-Sections
    • Test Your Learning
  • 9
    Type 8: Length of a Curve
    • The Formula for the Length of a Curve
    • Integrating with respect to Y to calculate the Length of a Curve
    • Integrating with respect to Time
    • Test Your Learning
  • 10
    Type 9: Rectilinear Motion
    • Calculate Position by Integrating Velocity
    • Calculate Position & Velocity by Integrating Acceleration
    • Solved Examples Involving Constant Acceleration
    • Test Your Learning
  • 11
    Type 10: Trigonometric Integration
    • Integrate Powers of sin x & cos x
    • Integrate Powers of tan x & sec x
    • Using Double Angle Formulas for Integration
    • Test Your Learning
  • 12
    Type 11: Integration by Parts
    • Integration by Parts in 3 Easy Steps
    • How to Apply Integration by Parts Twice
    • How to Simplify Tedious Problems using the Tabular Method
    • Test Your Learning
  • 13
    Type 12: Partial Fractions
    • The Basic Method of Partial Fractions
    • How to Decompose Repeated Factors
    • Important Techniques to Factor Polynomials
    • Partial Fractions for Quadratic Factors
    • Test Your Learning
  • 14
    Type 13: Advanced Integration Techniques
    • Reduction Formulas for powers of sin x, cos x, tan x & sec x
    • Trigonometric Substitution
    • Test Your Learning
  • 15
    Type 14: Differential Equations
    • Separation of Variables
    • Exponential Models of Growth and Decay
    • How to Draw Slope Fields using Isoclines
    • Test Your Learning
  • 16
    Type 15 Polar Coordinates
    • How to Convert between (x,y) and (r, theta) Coordinates
    • How to Calculate the Length of a Polar Curve
    • How to Calculate the Area Enclosed in a Polar Curve
    • How to Calculate the Area Enclosed between Two Curves
    • Test Your Learning
  • 17
    Type 16: Sequences & Series
    • Monotonic & Bounded Sequences
    • Geometric Series
    • Test Your Learning
  • 18
    Type 17: Taylor & Maclaurin Series
    • Using Taylor Series to Approximate Functions
    • Using Maclaurin Series to Approximate Functions
    • Test Your Learning
  • 19
    Next steps
    • Practice Workbook