Calculus 2

Integration techniques, series, and parametric equations

242Modules

6Units

Prerequisite:Calculus 1

Integration Techniques

Advanced methods for finding antiderivatives

46 modules

When Calculus Hits Its LimitsINTRO

Radicals and Right TrianglesINTRO

Power Reduction ArsenalINTRO

Chains Within ChainsINTRO

Advanced U-SubstitutionLESSON

The Parts FormulaLESSON

Repeated Integration by PartsLESSON

Integration by Parts MasteryPRACTICE

Strategies for Trig IntegralsLESSON

Trigonometric Integral LaboratoryACTIVITY

Secant and Tangent IntegralsLESSON

Completing the Square FirstLESSON

Trigonometric Function SubstitutionsLESSON

Trigonometric Substitution PracticePRACTICE

Three Key SubstitutionsLESSON

Decomposition StrategiesLESSON

Repeated FactorsLESSON

Riemann Sums RevisitedLESSON

The Trapezoidal RuleLESSON

Simpson's Rule - Parabolic PrecisionLESSON

Breaking Apart FractionsREAL WORLD

Reversing the Product RuleREAL WORLD

Decomposing (2x + 3)/((x - 1)(x + 2))EXAMPLE

Solving ∫x²sin(x)dxEXAMPLE

Integrating ∫dx/√(4 - x²)EXAMPLE

Integrating x³/((x² + 1)(x - 1)²)EXAMPLE

Approximating ∫₀² e^(-x²)dxEXAMPLE

Products of Sines and CosinesEXAMPLE

Area Under √(9 - x²)EXAMPLE

Evaluating ∫x√(x² + 1)dxEXAMPLE

Integrating ∫xe^x dxEXAMPLE

Evaluating ∫sin³(x)cos²(x)dxEXAMPLE

Parts vs Substitution DeciderACTIVITY

Error Bound ExplorerACTIVITY

Numerical Integration CalculatorACTIVITY

Partial Fraction DecomposerACTIVITY

The Cover-Up MethodACTIVITY

Substitution Triangle BuilderACTIVITY

Substitution Pattern RecognizerACTIVITY

Partial Fractions PracticePRACTICE

Substitution Strategy PracticePRACTICE

Trigonometric Integration PracticePRACTICE

Numerical Methods PracticePRACTICE

Integration Techniques SummarySUMMARY

Integration Techniques ReferenceFORMULA SHEET

Section 1 AssessmentQUIZ

Applications of Integration

Arc length, surface area, work, and fluid pressure

43 modules

Measuring Curved PathsINTRO

Spinning into SolidsINTRO

Stacking InfinitesimalsINTRO

Area Between Curves FormulaLESSON

Area Between Curves PracticePRACTICE

Horizontal IntegrationLESSON

The Slicing MethodLESSON

The Disk MethodLESSON

The Washer MethodLESSON

Washer Cross SectionsLESSON

Cross Section Volumes PracticePRACTICE

Volume with Square Cross SectionsEXAMPLE

The Shell MethodLESSON

Arc Length FormulaLESSON

Arc Length CalculatorACTIVITY

Arc Length and Surface Area PracticePRACTICE

Parametric Arc LengthLESSON

Surface Area of RevolutionLESSON

Revolution Method SelectorACTIVITY

Solids of Revolution PracticePRACTICE

Surface Area of SphereEXAMPLE

Spring Work FormulaLESSON

Center of MassLESSON

Hydrostatic PressureLESSON

Work as IntegrationREAL WORLD

Volume of Gabriel's HornREAL WORLD

From 2D to 3DREAL WORLD

Pressure on Vertical PlateEXAMPLE

Pumping Water from TankEXAMPLE

Length of y = x^(3/2) from 0 to 4EXAMPLE

Rotating y = x² from 0 to 2 Around y-axisEXAMPLE

Region Between y = x and y = x² Rotated Around x-axisEXAMPLE

Rotating y = √x Around x-axisEXAMPLE

Area of Region Bounded by x = y² - 2 and x = yEXAMPLE

Finding Area Between y = x² and y = √xEXAMPLE

Physics Problem SolverACTIVITY

Minimal Surfaces ExplorerACTIVITY

3D Solid BuilderACTIVITY

Interactive Area FinderACTIVITY

Work and Fluid Pressure PracticePRACTICE

Applications of Integration SummarySUMMARY

Applications of Integration ReferenceFORMULA SHEET

Section 2 AssessmentQUIZ

Sequences and Series

Infinite sequences, series, and convergence tests

50 modules

Functions as Infinite PolynomialsINTRO

The Convergence Test ToolkitINTRO

Patterns to InfinityINTRO

Sequences and Their LimitsLESSON

Sequence Limit ExplorerACTIVITY

Monotonic and Bounded SequencesLESSON

Recursive SequencesLESSON

Series FundamentalsLESSON

The Geometric SeriesLESSON

Telescoping SeriesLESSON

Harmonic Series DivergenceLESSON

The Divergence TestLESSON

The Integral TestLESSON

Comparison TestsLESSON

The Ratio TestLESSON

The Root TestLESSON

Alternating Series TestLESSON

Power Series DefinitionLESSON

Finding Interval of ConvergenceLESSON

Geometric Series as Power SeriesLESSON

Power Series ManipulationsLESSON

Taylor PolynomialsLESSON

Taylor Polynomial VisualizerACTIVITY

Taylor Series DerivationLESSON

Binomial SeriesLESSON

Series Solutions to Differential EquationsLESSON

Local Polynomial ApproximationREAL WORLD

From Sequences to SeriesREAL WORLD

Maclaurin Series for e^xEXAMPLE

Taylor Series for ln(x) at a = 1EXAMPLE

Interval for Σ(x^n/n)EXAMPLE

Testing Σ(n!/nⁿ)EXAMPLE

Testing Σ(1/n²)EXAMPLE

Evaluating Σ(2/3)ⁿ from n=0 to ∞EXAMPLE

Fibonacci Ratio ConvergenceEXAMPLE

Analyzing aₙ = n/(n+1)EXAMPLE

Function Series LibraryACTIVITY

Series for Common FunctionsACTIVITY

Power Series Convergence ExplorerACTIVITY

Test Selection StrategyACTIVITY

Convergence Test LaboratoryACTIVITY

Series Partial Sum CalculatorACTIVITY

Series Applications PracticePRACTICE

Power Series PracticePRACTICE

Convergence Tests PracticePRACTICE

Series Convergence Basics PracticePRACTICE

Sequence Convergence PracticePRACTICE

Sequences and Series SummarySUMMARY

Series and Sequences ReferenceFORMULA SHEET

Section 3 AssessmentQUIZ

Parametric and Polar

Alternative coordinate systems and vectors

42 modules

Slopes on Polar CurvesINTRO

Curves in MotionINTRO

Parametric RepresentationLESSON

Derivatives of Parametric CurvesLESSON

Arc Length of Parametric CurvesLESSON

Polar Coordinate SystemLESSON

Graphing Polar CurvesLESSON

Polar Graphing PracticePRACTICE

Graphing r = 2 + 2cos(θ)EXAMPLE

Rose Curves r = a·cos(nθ)LESSON

Derivatives in Polar FormLESSON

Area in Polar CoordinatesLESSON

Area Between Polar CurvesLESSON

Arc Length in PolarLESSON

Conic Sections in PolarLESSON

Vector FundamentalsLESSON

Dot ProductLESSON

Work as Dot ProductREAL WORLD

Vector ProjectionsLESSON

Magnitude and DirectionREAL WORLD

Beyond CartesianREAL WORLD

Finding Angle Between VectorsEXAMPLE

Vector OperationsEXAMPLE

Length of Spiral r = e^θEXAMPLE

Tangent to r = 1 + sin(θ) at θ = π/6EXAMPLE

Area Inside r = 1 + cos(θ)EXAMPLE

Converting Between SystemsEXAMPLE

Finding Tangent to CycloidEXAMPLE

Graphing x = t² - 2t, y = t + 1EXAMPLE

Vector Problem SolverACTIVITY

Vector Addition LaboratoryACTIVITY

Polar Calculus VisualizerACTIVITY

Polar Curve GalleryACTIVITY

Polar Grid ExplorerACTIVITY

Projectile Motion LaboratoryACTIVITY

Parametric Curve TracerACTIVITY

Vector Applications PracticePRACTICE

Polar Calculus PracticePRACTICE

Parametric Curves PracticePRACTICE

Alternative Coordinate Systems SummarySUMMARY

Parametric, Polar, and Vector ReferenceFORMULA SHEET

Section 4 AssessmentQUIZ

Differential Equations

First and second-order equations and applications

54 modules

Beyond First-OrderINTRO

Limited ResourcesINTRO

Natural Growth PatternsINTRO

Step-by-Step ApproximationINTRO

Splitting and IntegratingINTRO

Equations with DerivativesINTRO

What is a Differential Equation?LESSON

Differential Equations PracticePRACTICE

Slope FieldsLESSON

Slope Field ExplorerACTIVITY

Sketching Solutions on Slope FieldsEXAMPLE

Initial Value ProblemsLESSON

Separation MethodLESSON

Orthogonal TrajectoriesLESSON

Euler's Method AlgorithmLESSON

Euler's Method CalculatorACTIVITY

Euler's Method PracticePRACTICE

Improved Euler's MethodLESSON

The Exponential ModelLESSON

Exponential Model SimulatorACTIVITY

Exponential Models PracticePRACTICE

Modified Exponential ModelsLESSON

The Logistic ModelLESSON

Logistic Model FittingACTIVITY

Solving the Logistic EquationLESSON

Maximum Growth RateLESSON

Second-Order Linear EquationsLESSON

Second-Order Equations PracticePRACTICE

Complex Roots and OscillationsLESSON

Damped OscillationsREAL WORLD

Resonance PhenomenonLESSON

Disease Spread (SIR Model Preview)REAL WORLD

Carbon DatingREAL WORLD

When Exact Solutions Don't ExistREAL WORLD

Population Growth ModelREAL WORLD

Simple Harmonic MotionEXAMPLE

Solving y'' - 5y' + 6y = 0EXAMPLE

Modeling Fish PopulationEXAMPLE

Population ExplosionEXAMPLE

Compound Interest as Continuous GrowthEXAMPLE

Approximating y(1) for dy/dx = x + y, y(0) = 1EXAMPLE

Newton's Law of CoolingEXAMPLE

Solving dy/dx = y²cos(x)EXAMPLE

Verifying SolutionsEXAMPLE

Characteristic Equation SolverACTIVITY

Logistic vs ExponentialACTIVITY

Error Analysis VisualizerACTIVITY

Separation of Variables SolverACTIVITY

Solution VerifierACTIVITY

Logistic Growth PracticePRACTICE

Separable Equations PracticePRACTICE

Differential Equations SummarySUMMARY

Differential Equations ReferenceFORMULA SHEET

Section 5 AssessmentQUIZ

Course Conclusion

Review and preview of future topics

7 modules

Course Achievement PortfolioACTIVITY

Series Convergence DiagnosticACTIVITY

Integration Techniques TournamentACTIVITY

Graduate-Level PreviewSUMMARY

Calculus 2 Connections MapSUMMARY

Complete Formula CompendiumFORMULA SHEET

Calculus 2 Mastery ExamQUIZ