AP®︎ Calculus BC: Topic 6.3 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 6.3 of AP Calculus BC – Riemann Sums, Summation Notation, and Definite Integral Notation.
Questions List
Topic 6.3
Question 1 Easy
What is the value of ?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Topic 6.3: Riemann Sums, Summation Notation, and Definite Integral Notation
Learning Objective: LIM-5.B
Interpret the limiting case of the Riemann sum as a definite integral.
Essential Knowledge: LIM-5.B.1
The limit of an approximating Riemann sum can be interpreted as a definite integral.
Essential Knowledge: 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.
Learning Objective: LIM-5.C
Represent the limiting case of the Riemann sum as a definite integral.
Essential Knowledge: LIM-5.C.1
The definite integral of a continuous function f over the interval [a, b], denoted by ∫_a^b f(x) dx, is the limit of Riemann sums as the widths of the subintervals approach 0. That is, ∫_a^b f(x) dx = lim_{max Δx_i → 0} Σ_{i=1}^n f(x_i^*) Δx_i, where n is the number of subintervals, Δx_i is the width of the ith subinterval, and x_i^* is a value in the ith subinterval.
Essential Knowledge: 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.
