AP Calculus AB 6.3 Riemann Sums Summation Notation and Definite Integral Notation Questions

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: $\lim_{n\to\infty}\sum_{k=1}^{n}\left(\frac{3k}{n}+2\right)^{2}\left(\frac{3}{n}\right)$ .

$\int_{2}^{5}(x+2)^{2}\,dx$

$\int_{0}^{3}(3x+2)^{2}\,dx$

$\int_{2}^{5}x^{2}\,dx$

$\int_{0}^{3}x^{2}\,dx$

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Covered syllabus points

Question 1

Question 2