AP Calculus BC 6.3: Riemann Sums as Definite Integrals

Practise translating between limits of Riemann sums and definite integrals by matching the integrand, interval endpoints, sample points, and subinterval width.

Exam points

Translate a Riemann-sum limit into a definite integral by matching Δx, bounds, and sample points.
Rewrite a definite integral as a Riemann-sum limit with the correct interval width and shifted inputs.

[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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LIM-5.C—Represent the limiting case of the Riemann sum as a definite integral question 1