Compute the Riemann sum £f(x;)Aæ for f(æ) = a² , [a, b] = [0, 1]. i=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Compute the Riemann sum**
\[
\sum_{i=1}^{n} f(x_i) \Delta x \quad \text{for} \quad f(x) = x^2, \, [a, b] = [0, 1].
\]
**Options:**
- ○ \(\frac{1}{3}\)
- ○ \(\frac{1}{6} \left(1 + \frac{1}{n}\right) \left(2 + \frac{1}{n}\right)\)
- ○ \(\frac{i^2}{n^3}\)
- ○ \(\frac{1}{3} \left(1 + \frac{1}{n}\right)^2\)
- ○ \(\frac{i}{n}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d31ea21-51a6-4893-9fcb-4fc7e3b87aa7%2F56bbb853-908c-4304-b0ab-be4e579a5aac%2F7l9nl9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Compute the Riemann sum**
\[
\sum_{i=1}^{n} f(x_i) \Delta x \quad \text{for} \quad f(x) = x^2, \, [a, b] = [0, 1].
\]
**Options:**
- ○ \(\frac{1}{3}\)
- ○ \(\frac{1}{6} \left(1 + \frac{1}{n}\right) \left(2 + \frac{1}{n}\right)\)
- ○ \(\frac{i^2}{n^3}\)
- ○ \(\frac{1}{3} \left(1 + \frac{1}{n}\right)^2\)
- ○ \(\frac{i}{n}\)
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