AP Calculus AB 6.3 Riemann Sums and Integrals Overview

Connect Riemann sums with definite integrals by interpreting limiting sums and representing integrals with summation notation.

Exam points

interpret a Riemann sum as accumulated area or a definite integral
translate between summation notation, limits and definite-integral notation

Covered syllabus points

LIM-5.B—Interpret 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

[Maximum number: 1]

For a certain continuous function f, the right Riemann sum approximation of $\int_{0}^{2} f(x) d x$ with n subintervals of equal length is $\frac{2(n+1)(3 n+2)}{n^{2}}$ for all n. What is the value of $\int_{0}^{2} f(x) d x$ ?

$Graph of $f$$

Graph of $f$

[Maximum number: 1]

Choose the integral that is the limit of the Riemann Sum: nit n approaches to infinity of sum from k equals 1 to n of left parenthesis left parenthesis start fraction numerator 3 k over denominator n end fraction plus 2 right parenthesis squared end exponent times left parenthesis 3 over n right parenthesis right parenthesis .

(A) ategral from 2 to 5 of left parenthesis x plus 2 right parenthesis squared end exponent d x

(B) ategral from 0 to 3 of left parenthesis 3 x plus 2 right parenthesis squared end exponent d x

(D) ategral from 0 to 3 of x squared end exponent dx

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Covered syllabus points

6.3 Riemann Sums, Summation Notation, and Definite Integral Notation question 1

6.3 Riemann Sums, Summation Notation, and Definite Integral Notation question 2