Public learning track
Antiderivatives and Indefinite Integrals Foundations
10th Grade · Math · Open Global Math
8 lessons
Goal
Apply linearity properties and basic integration rules to evaluate indefinite integrals for polynomials, 1/x, e^x, sin(x), and cos(x), and solve initial value problems.
Featured Diagrams
Antiderivatives and Indefinite Integrals
8 lessons
0 of 8 done
- 1Antiderivatives and Indefinite IntegralsUp nextStart
- 2Linearity Properties of Indefinite IntegralsPremiumNot started yet
- 3The Power Rule for Integration and Polynomial IntegralsNot started yet
- 4Integrating Rational Expressions Leading to Logarithmic Forms: 1/xNot started yet
- 5Integration of Exponential and Logarithmic FunctionsNot started yet
- 6Integrating Trigonometric, Exponential and Logarithmic FunctionsNot started yet
- 7Finding Particular Antiderivatives Using Initial Conditions and Boundary ValuesNot started yet
- 8Motion Problems with Antiderivatives: Position, Velocity, and AccelerationNot started yet
Standards Covered
- OGM.11.CAL.3Open Global Math Standards 2026™ · Math · Level 11 / High School 2 (Age 15) · Grade 10Prove and apply linearity properties of antiderivatives (primitives) and basic indefinite integrals for polynomial combinations, 1/x, e^x, sin(x), and cos(x).
- OGM.11.CAL.2Open Global Math Standards 2026™ · Math · Level 11 / High School 2 (Age 15) · Grade 10Interpret derivatives as average and instantaneous rates of change and tangent slopes; compute first and second derivatives of polynomial, rational, exponential, logarithmic, and trigonometric functions; and apply derivatives to curve sketching (concavity, inflection points) and optimization problems.
Curriculum Framework
10th Grade · Math · Open Global Math
1
14 lessons
Limits, Continuity, and Asymptotic Behavior
Evaluate limits algebraically and numerically, analyze continuity, determine all types of asymptotes, and resolve indeterminate forms using L'Hopital's rule.
2
14 lessons
Differential Calculus Foundations and Differentiation Rules
Compute first and second derivatives of polynomial, rational, exponential, logarithmic, and trigonometric functions using analytical rules.
3
10 lessons
Applications of Derivatives: Curve Sketching and Optimization
Apply first and second derivatives to analyze monotonicity, concavity, points of inflection, graph behavior, and solve real-world optimization problems.
4
8 lessons
Antiderivatives and Indefinite Integrals Foundations
Apply linearity properties and basic integration rules to evaluate indefinite integrals for polynomials, 1/x, e^x, sin(x), and cos(x), and solve initial value problems.