AP Calculus BC 6.3 Riemann Sum Notation Question Bank

Match interval widths, bounds and sample points to translate Riemann-sum limits into definite integrals and back again, keeping the indexing and scaling consistent.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

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]

29. Choose the integral that is the limit of the Riemann Sum: $\lim _{n \rightarrow \infty} \sum_{k=1}^{n}\left(\left(\frac{3 k}{n}+2\right)^{2} \cdot\left(\frac{3}{n}\right)\right)$ .

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

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

$\int_{2}^{5} x^{2} d x$

$\int_{0}^{3} x^{2} d x$ STOP If there is still time remaining, you may review your answers. Part B TIME: 38 MINUTES Some questions in this part of the examination require the use of a graphing calculator. There are 13 questions in Part B, for which 38 minutes are allowed. Because there is no deduction for wrong answers, you should answer every question, even if you need to guess. DIRECTIONS: Choose the best answer for each question. If the exact numerical value of the correct answer is not listed as a choice, select the choice that is closest to the exact numerical answer.

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Covered syllabus points

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