Public learning track
Definite Integrals and the Fundamental Theorem of Calculus
12th Grade · Math · Open Global Math
8 lessons
Goal
Understand integration as the limit of Riemann sums, apply the Fundamental Theorem of Calculus, and integrate standard function families.
Featured Diagrams
Approximating Area with Riemann Sums: Left, Right, and Midpoint
8 lessons
0 of 8 done
- 1Approximating Area with Riemann Sums: Left, Right, and MidpointUp nextStart
- 2The Definite Integral as the Limit of a Riemann SumPremiumNot started yet
- 3The Fundamental Theorem of Calculus: Evaluation PartNot started yet
- 4The Fundamental Theorem of Calculus: Differentiating Integral FunctionsNot started yet
- 5Integrating Polynomial and General Power FunctionsNot started yet
- 6Integrating Exponential Functions: Base e and General BasesNot started yet
- 7Integrating Reciprocal Functions Yielding Natural LogarithmsNot started yet
- 8Integrating Sine and Cosine FunctionsNot started yet
Curriculum Framework
12th Grade · Math · Open Global Math
1
7 lessons
Limits, First Principles, and Derivative Foundations
Understand derivatives as limits of difference quotients, differentiate fundamental functions from first principles, and interpret first and second derivatives geometrically.
2
11 lessons
Differentiation Rules and Transcendental Functions
Differentiate power, exponential, logarithmic, and trigonometric functions using product, quotient, chain, and inverse differentiation rules.
3
7 lessons
Implicit Differentiation, Parametric Curves, and Related Rates
Differentiate implicit relations and parametric equations, and solve connected rates of change problems.
4
7 lessons
Applications of Derivatives: Extrema and Optimization
Determine tangent and normal equations, find extrema, analyze curve behavior, and solve real-world optimization problems.
5
8 lessons
Definite Integrals and the Fundamental Theorem of Calculus
Understand integration as the limit of Riemann sums, apply the Fundamental Theorem of Calculus, and integrate standard function families.
6
8 lessons
Advanced Integration Techniques: Substitution, Parts, and Partial Fractions
Master advanced integration methods including u-substitution, integration by parts, and partial fractions for definite and indefinite integrals.
7
6 lessons
Area Under Curves and Between Intersecting Functions
Evaluate definite integrals to calculate the total geometric area under a curve and enclosed between intersecting curves.
8
9 lessons
Differential Equations and Mathematical Modeling
Formulate first-order differential equations from contextual scenarios, find general and particular solutions via separation of variables, and analyze model behavior.