Public learning track
Definite Integrals, Riemann Sums, and the Fundamental Theorem of Calculus
11th Grade · Math · Open Global Math
8 lessons
Goal
Interpret definite integrals as limits of Riemann sums, apply the Fundamental Theorem of Calculus, and calculate areas under and between curves.
Featured Diagrams
Riemann Sums and the Limit Definition of the Definite Integral
8 lessons
0 of 8 done
- 1Riemann Sums and the Limit Definition of the Definite IntegralUp nextStart
- 2Definite Integrals and the Fundamental Theorem of CalculusPremiumNot started yet
- 3Standard Algebraic Integrals and the Reverse Chain RuleNot started yet
- 4Integrating Exponential and Reciprocal FunctionsNot started yet
- 5Integrating Trigonometric Functions: Sine, Cosine, and Secant SquaredNot started yet
- 6Finding Particular Antiderivatives Using Initial Conditions and Boundary ValuesNot started yet
- 7Calculating Areas Under Curves Above and Below the x-AxisNot started yet
- 8Calculating Areas Between Intersecting CurvesNot started yet
Standards Covered
- OGM.12.CAL.4Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Understand the Fundamental Theorem of Calculus and integration as the limit of a Riemann sum; evaluate definite and indefinite integrals of standard algebraic, exponential, reciprocal (1/x), and trigonometric functions; calculate areas under curves and between intersecting curves.
- OGM.12.CAL.6Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Construct and solve first-order differential equations with separable variables dy/dx = f(x)g(y); determine general and particular solutions with initial conditions; interpret solutions in kinematics, growth/decay, and physical contexts.
Curriculum Framework
11th Grade · Math · Open Global Math
1
7 lessons
First Principles and Foundations of Derivatives
Derive the derivative definition from difference quotients, prove standard derivatives from first principles, and analyze second derivatives and curvature.
2
11 lessons
Advanced Differentiation Rules and Transcendental Functions
Differentiate exponential, logarithmic, and trigonometric functions using chain, product, and quotient rules.
3
7 lessons
Implicit and Parametric Differentiation and Rates of Change
Differentiate implicit equations and parametric curves, and solve connected rates of change modeling problems.
4
8 lessons
Applications of Derivatives: Tangents, Extrema, and Curve Sketching
Construct tangent and normal lines, classify local and global extrema, and sketch complex transcendental curves.
5
8 lessons
Definite Integrals, Riemann Sums, and the Fundamental Theorem of Calculus
Interpret definite integrals as limits of Riemann sums, apply the Fundamental Theorem of Calculus, and calculate areas under and between curves.
6
9 lessons
Advanced Integration Techniques: Substitution, Parts, and Partial Fractions
Evaluate non-standard integrals using algebraic substitution, integration by parts, and partial fraction decompositions.
7
6 lessons
First-Order Differential Equations and Modeling
Formulate, solve, and interpret separable first-order differential equations in physical, biological, and kinematic contexts.
8
7 lessons
Numerical Calculus and Iterative Methods
Locate roots via sign change, solve equations using fixed-point iteration and Newton-Raphson, and approximate integrals with the trapezium rule.