LIM-5.C—Represent the limiting case of the Riemann sum as a definite integral
- Syllabus
- 2020
- Objective
- —
- Level
- —
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.
ConceptAP Calculus BC