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AP Calculus AB Lim 5 B Interpret the Limiting Case of the Riemann Sum As a Definite Integral Questions

Interpret a limiting Riemann sum as a definite integral, identify its bounds and integrand, and use the limit expression to determine the integral value.

Syllabus
Effective Fall 2020
Course
AP Calculus AB

Exam points

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

AP Calculus AB Lim 5 B Interpret the Limiting Case of the Riemann Sum As a Definite Integral Questions question 1

[Maximum number: 1]

For a certain continuous function f, the right Riemann sum approximation of ∫02f(x)dx\int_{0}^{2} f(x) d x with n subintervals of equal length is 2(n+1)(3n+2)n2\frac{2(n+1)(3 n+2)}{n^{2}} for all n. What is the value of ∫02f(x)dx\int_{0}^{2} f(x) d x ?

Graph of \(f\)

Graph of \(f\)

A

2

B

6

C

12

D

20

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