6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
- Syllabus
- 2020
- Topic
- 6.3
- Level
- —
LIM-5.B—Interpret the limiting case of the Riemann sum as a definite integral
- LIM-5.B Interpret the limiting case of the Riemann sum as a definite integral.
- LIM-5.B.1 The limit of an approximating Riemann sum can be interpreted as a definite integral.
- LIM-5.B.2 A Riemann sum, which requires a partition of an interval I, is the sum of products, each of which is the value of the function at a point in a subinterval multiplied by the length of that subinterval of the partition.
- Enduring understanding LIM-5: Definite integrals can be approximated using geometric and numerical methods.
LIM-5.C—Represent the limiting case of the Riemann sum as a definite integral
- LIM-5.C Represent the limiting case of the Riemann sum as a definite integral.
- LIM-5.C.1 The definite integral of a continuous function f over the interval [a, b], denoted by ∫ₐᵇ f(x)dx, is the limit of Riemann sums as the widths of the subintervals approach 0. That is, ∫ₐᵇ f(x)dx = lim(max Δxᵢ→0) Σ(i=1 to n) f(xᵢ*)Δxᵢ, where n is the number of subintervals, Δxᵢ is the width of the ith subinterval, and xᵢ* is a value in the ith subinterval.
- LIM-5.C.2 A definite integral can be translated into the limit of a related Riemann sum, and the limit of a Riemann sum can be written as a definite integral.
- Enduring understanding LIM-5: Definite integrals can be approximated using geometric and numerical methods.
Objective notes
2 learning objectivesConceptAP Calculus BC