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

Translate a limiting Riemann sum into definite integral notation by identifying the function, interval, sample points and subinterval width.

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 C Represent the Limiting Case of the Riemann Sum As a Definite Integral Questions question 1

[Maximum number: 1]

Choose the integral that is the limit of the Riemann Sum: lim⁡n→∞∑k=1n(3kn+2)2(3n)\lim_{n\to\infty}\sum_{k=1}^{n}\left(\frac{3k}{n}+2\right)^{2}\left(\frac{3}{n}\right).

A

∫25(x+2)2 dx\int_{2}^{5}(x+2)^{2}\,dx

B

∫03(3x+2)2 dx\int_{0}^{3}(3x+2)^{2}\,dx

C

∫25x2 dx\int_{2}^{5}x^{2}\,dx

D

∫03x2 dx\int_{0}^{3}x^{2}\,dx

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