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Calculus 2 · Lessons

Calculus 2 lessons

7 sections · 75 skills · work through the full outline skill by skill — read the long-form lesson or flip through the slide-style version.
Long-form lessonsSlide-style lessons

Calculus 2

Practice 75 skills across this outline.

Recommended next
Cross Sections: Triangles & Semicircles
Applications of Integration · Volumes of Solids
Long-form lesson
Weighting distribution
20 categories
Integration Foundations
14%
Problem-Solving & Modeling Tools
14%
Techniques of Integration · General Skills
10%
Applications of Integration · Volumes of Solids
9%
Parametric, Polar & Vector Functions · Parametric Curves
9%
Sequences & Series · Convergence Tests
7%

Skills

The comprehensive taxonomy of calculus 2 — drill into a card to work its skills.

Applications of Integration · Volumes of Solids

7 core skills9% total weight
0/7 completed
7 skills to mastery
1
Cross Sections: Triangles & SemicirclesRecommended
Long-form
2
Washer Method: x- or y-AxisAvailable
Long-form
3
Disc Method: Other AxesAvailable
Long-form
4
Washer Method: Other AxesAvailable
Long-form
5
Disc Method: x- or y-AxisAvailable
Long-form
6
Shell MethodAvailable
Long-form
7
Cross Sections: Squares & RectanglesAvailable
Long-form

Applications of Integration · Applications of Integration

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Arc Length & Distance TraveledAvailable
Long-form
2
Surface Area of RevolutionAvailable
Long-form
3
Arc Length (Cartesian)Available
Long-form

Applications of Integration · Area Between Curves

3 core skills1% total weight
0/3 completed
3 skills to mastery
1
Area Between Multiple IntersectionsAvailable
Long-form
2
Area Between Curves (x-functions)Available
Long-form
3
Area Between Curves (y-functions)Available
Long-form

Applications of Integration · General Skills

3 core skills2% total weight
0/3 completed
3 skills to mastery
1
Average Value of a FunctionAvailable
Long-form
2
Position, Velocity, Acceleration via IntegralsAvailable
Long-form
3
Accumulation Functions in ContextAvailable
Long-form

Parametric, Polar & Vector Functions · Polar Coordinates and Curves

4 core skills1% total weight
0/4 completed
4 skills to mastery
1
Area of a Polar RegionAvailable
Long-form
2
Polar Coordinates & DifferentiationAvailable
Long-form
3
Slope & Tangent Lines in PolarAvailable
Long-form
4
Area Between Two Polar CurvesAvailable
Long-form

Parametric, Polar & Vector Functions · Vector-Valued Functions

2 core skills4% total weight
0/2 completed
2 skills to mastery
1
Vector-Valued Functions & DerivativesAvailable
Long-form
2
Integrating Vector-Valued FunctionsAvailable
Long-form

Parametric, Polar & Vector Functions · Parametric Curves

5 core skills9% total weight
0/5 completed
5 skills to mastery
1
Area Between Parametric CurvesAvailable
Long-form
2
Second Derivatives: ParametricAvailable
Long-form
3
Arc Length of Parametric CurvesAvailable
Long-form
4
Motion with Parametric & Vector FunctionsAvailable
Long-form
5
Parametric Equations & DerivativesAvailable
Long-form

Sequences & Series · Convergence Tests

7 core skills7% total weight
0/7 completed
7 skills to mastery
1
Ratio TestAvailable
Long-form
2
Comparison TestsAvailable
Long-form
3
Integral TestAvailable
Long-form
4
Absolute vs. Conditional ConvergenceAvailable
Long-form
5
Alternating Series TestAvailable
Long-form
6
Radius & Interval of ConvergenceAvailable
Long-form
7
nth Term Test for DivergenceAvailable
Long-form

Sequences & Series · Power Series and Taylor Series

4 core skills2% total weight
0/4 completed
4 skills to mastery
1
Taylor Polynomial ApproximationsAvailable
Long-form
2
Taylor & Maclaurin SeriesAvailable
Long-form
3
Representing Series as Power SeriesAvailable
Long-form
4
Taylor & Maclaurin ExpansionsAvailable
Long-form

Sequences & Series · Sequences and Series Foundations

2 core skills2% total weight
0/2 completed
2 skills to mastery
1
Convergent & Divergent SeriesAvailable
Long-form
2
Sequence Convergence & LimitsAvailable
Long-form

Sequences & Series · Error Bounds and Approximations

2 core skills1% total weight
0/2 completed
2 skills to mastery
1
Alternating Series Error BoundAvailable
Long-form
2
Lagrange Error BoundAvailable
Long-form

Sequences & Series · General Skills

2 core skills2% total weight
0/2 completed
2 skills to mastery
1
Geometric SeriesAvailable
Long-form
2
Harmonic & p-SeriesAvailable
Long-form

Integration Foundations

9 core skills14% total weight
0/9 completed
9 skills to mastery
1
Integration: Long Division & Completing SquareAvailable
Long-form
2
Accumulations of ChangeAvailable
Long-form
3
Selecting Integration TechniquesAvailable
Long-form
4
Riemann Sums & NotationAvailable
Long-form
5
FTC & Definite IntegralsAvailable
Long-form
6
Accumulation Function BehaviorAvailable
Long-form
7
FTC & Accumulation FunctionsAvailable
Long-form
8
Properties of Definite IntegralsAvailable
Long-form
9
Riemann Sum ApproximationsAvailable
Long-form

Techniques of Integration · General Skills

6 core skills10% total weight
0/6 completed
6 skills to mastery
1
Improper IntegralsAvailable
Long-form
2
Linear Partial FractionsAvailable
Long-form
3
Partial Fractions: Repeated & QuadraticsAvailable
Long-form
4
Integration by SubstitutionAvailable
Long-form
5
Choosing Integration MethodsAvailable
Long-form
6
Integration by PartsAvailable
Long-form

Techniques of Integration · Trigonometric Integrals

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
Trig SubstitutionAvailable
Long-form
2
Integrating tan & sec ProductsAvailable
Long-form
3
Integrating sin & cos ProductsAvailable
Long-form

Differential Equations · General Skills

2 core skills4% total weight
0/2 completed
2 skills to mastery
1
Logistic ModelsAvailable
Long-form
2
Exponential Growth and Decay ModelsAvailable
Long-form

Differential Equations · Slope Fields and Qualitative Solutions

2 core skills4% total weight
0/2 completed
2 skills to mastery
1
Reasoning with Slope FieldsAvailable
Long-form
2
Sketching Slope FieldsAvailable
Long-form

Differential Equations · Differential Equations Basics

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Verifying DE SolutionsAvailable
Long-form
2
Euler's MethodAvailable
Long-form
3
Modeling with Differential EquationsAvailable
Long-form

Differential Equations · Separable Differential Equations

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
General Solutions: Separation of VariablesAvailable
Long-form
2
Solving Separable DEsAvailable
Long-form
3
Particular Solutions: Initial ConditionsAvailable
Long-form

Problem-Solving & Modeling Tools

3 core skills14% total weight
0/3 completed
3 skills to mastery
1
Approximation Error & BoundsAvailable
Long-form
2
Algebraic & Trig SimplificationAvailable
Long-form
3
Interpreting Graphs for SetupAvailable
Long-form