Public learning track
Numerical Integration and Approximation Bounds
12th Grade · Math · Open Global Math
5 lessons
Goal
Approximate definite integrals using the Trapezium Rule, determine upper and lower bounds, analyze error behavior from curve convexity, and solve contextual problems.
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Numerical Integration Using the Trapezium Rule
5 lessons
0 of 5 done
- 1Numerical Integration Using the Trapezium RuleUp nextStart
- 2Over- and Under-Estimation in the Trapezium RulePremiumNot started yet
- 3Establishing Upper and Lower Bounds for Definite IntegralsNot started yet
- 4Approximating Integrals from Discrete and Experimental DataNot started yet
- 5Solving Real-World Engineering and Environmental Problems with Numerical MethodsNot started yet
Standards Covered
- OGM.13.NUMA.2Open Global Math Standards 2026™ · Math · Level 13 / High School 4 (Age 17–18) · Grade 12Approximate definite integrals and areas under curves numerically using the Trapezium (Trapezoidal) Rule; determine bounds and assess errors, limitations, and degrees of accuracy in contextual problems.
- OGM.13.NUMA.1Open Global Math Standards 2026™ · Math · Level 13 / High School 4 (Age 17–18) · Grade 12Locate roots of equations $f(x) = 0$ using sign-change intervals, simple fixed-point iteration $x_{n+1} = g(x_n)$ with staircase and cobweb diagrams, and the Newton-Raphson method; analyze circumstances and conditions under which these numerical schemes fail.
Curriculum Framework
12th Grade · Math · Open Global Math
1
9 lessons
Numerical Methods for Root Finding
Locate and approximate roots of algebraic and transcendental equations using sign-change tests, fixed-point iteration, and Newton-Raphson methods while evaluating convergence criteria and failure conditions.
2
5 lessons
Numerical Integration and Approximation Bounds
Approximate definite integrals using the Trapezium Rule, determine upper and lower bounds, analyze error behavior from curve convexity, and solve contextual problems.