Mr. Integral

Build methods and approximations

Calculus II

Choose integration methods, study infinite series, and use Taylor polynomials to approximate functions.

Start learning 6 units · 21 lessons

The course, unit by unit.

Open a unit for its introduction, map and lesson route.

01Integration MethodsChoose a technique from the structure of an integrand.5 lessons

Which integration method fits this structure?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Integration by Parts
  2. 02Integrating Trigonometric Powers
  3. 03Trigonometric Substitution and Branches
  4. 04Rational Integration and Partial Fractions
  5. 05Hyperbolic Functions and Inverse Integrals
02Geometry and Physical ApplicationsBuild areas, volumes, lengths, work and mass from small contributions.4 lessons

What should each tiny piece contribute?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Area Between Curves and Average Values
  2. 02Volumes of Revolution
  3. 03Arc Length and Surface Area
  4. 04Work, Density and Center of Mass
03Improper and Numerical IntegrationDecide convergence and control approximation error.2 lessons

When is an integral meaningful, and when is an estimate reliable?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Improper Integrals and Convergence
  2. 02Numerical Quadrature and Error Bounds
04Sequences and SeriesUnderstand infinite accumulation and choose a convergence test.4 lessons

Can infinitely many contributions have a finite total?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Sequences, Geometric and Telescoping Series
  2. 02Integral and Comparison Tests
  3. 03Ratio and Root Tests
  4. 04Alternating Series and Error Control
05Power Series and Taylor ApproximationRepresent functions with series and justify approximation accuracy.3 lessons

How can a polynomial stand in for a complicated function?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Power Series and Endpoint Tests
  2. 02Differentiating and Integrating Power Series
  3. 03Taylor Polynomials and Remainders
06Parametric and Polar CalculusStudy curves, motion and regions; finish with a mixed checkpoint.3 lessons

What if x is not the most useful input?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Parametric Curves and Motion
  2. 02Polar Curves, Area and Length
  3. 03Calculus II Checkpoint