By dragging all of the statements from the left column to the right column below, display a complete calculation of f2²dx using Riemann sums.
By dragging all of the statements from the left column to the right column below, display a complete calculation of f2²dx using Riemann sums.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![By dragging all of the statements from the left column to the right column below, display a complete calculation of the integral \(\int_2^5 x^2 dx\) using Riemann sums.
**Statements to choose from:** Drag these statements to the right column.
1. \(\lim_{n \to \infty} \left( 12 + 18 + 9 - \frac{9}{4n^2} \right)\)
2. \(\lim_{n \to \infty} \left( \frac{12}{n} + \frac{18}{n^2} n^2 + \frac{27}{4n^2} (4n^2 - 1) \right)\)
3. \(\lim_{n \to \infty} \sum_{k=1}^{n} \left[ \left( 4 + \frac{6}{n} (2k - 1) + \frac{9}{4n^2} (2k - 1)^2 \right) \frac{3}{n} \right]\)
4. \(\int_2^5 x^2 dx = \lim_{n \to \infty} \sum_{k=1}^{n} f(\bar{x}_k) \Delta x\)
5. \(= 12 + 18 + 9 - 0 = 39\)
6. \(\lim_{n \to \infty} \left( \frac{12}{n} \sum_{k=1}^{n} [1] + \frac{18}{n^2} \sum_{k=1}^{n} (2k - 1) + \frac{27}{4n^2} \sum_{k=1}^{n} (2k - 1)^2 \right)\)
7. \(\lim_{n \to \infty} \frac{n}{n} \left[ \frac{12}{n} + \frac{18}{n^2} (2k - 1) + \frac{27}{4n^2} (2k - 1)^2 \right]\)
8. \(= \lim_{n \to \infty} \sum_{k=1}^{n} \left[ \left( 2 + \frac{5 - 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ba37d91-3081-42ea-952f-3d2c5579a63d%2F2770ddc6-21f8-46b5-bb1a-4bb2c5aaefa1%2Flesipv7_processed.png&w=3840&q=75)
Transcribed Image Text:By dragging all of the statements from the left column to the right column below, display a complete calculation of the integral \(\int_2^5 x^2 dx\) using Riemann sums.
**Statements to choose from:** Drag these statements to the right column.
1. \(\lim_{n \to \infty} \left( 12 + 18 + 9 - \frac{9}{4n^2} \right)\)
2. \(\lim_{n \to \infty} \left( \frac{12}{n} + \frac{18}{n^2} n^2 + \frac{27}{4n^2} (4n^2 - 1) \right)\)
3. \(\lim_{n \to \infty} \sum_{k=1}^{n} \left[ \left( 4 + \frac{6}{n} (2k - 1) + \frac{9}{4n^2} (2k - 1)^2 \right) \frac{3}{n} \right]\)
4. \(\int_2^5 x^2 dx = \lim_{n \to \infty} \sum_{k=1}^{n} f(\bar{x}_k) \Delta x\)
5. \(= 12 + 18 + 9 - 0 = 39\)
6. \(\lim_{n \to \infty} \left( \frac{12}{n} \sum_{k=1}^{n} [1] + \frac{18}{n^2} \sum_{k=1}^{n} (2k - 1) + \frac{27}{4n^2} \sum_{k=1}^{n} (2k - 1)^2 \right)\)
7. \(\lim_{n \to \infty} \frac{n}{n} \left[ \frac{12}{n} + \frac{18}{n^2} (2k - 1) + \frac{27}{4n^2} (2k - 1)^2 \right]\)
8. \(= \lim_{n \to \infty} \sum_{k=1}^{n} \left[ \left( 2 + \frac{5 - 2
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