wherer € [1, 5]. Use 5 nodes to u intervals. 1. Use Trapezoid rule to approxim
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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![The function \( f(x) = \frac{\exp(x) - \exp(-x)}{\exp(x) + \exp(-x)} + \ln(x) \) is given, where \( x \in [1, 5] \).
1. **Trapezoid Rule**: Use the trapezoid rule to approximate the integral \(\int_1^5 f(x) \, dx\).
2. **Simpson’s Rule**: Use Simpson’s rule to approximate the integral \(\int_1^5 f(x) \, dx\).
3. **Gaussian Quadrature**: Use 2 Gaussian points (\( n = 1 \)) to evaluate the integration in each sub-interval and sum them up to get the integration over the entire domain.
The interval \([1, 5]\) is divided into 4 sub-intervals using 5 nodes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74ac81bd-2b81-497e-b1b6-4cc5e46be1b6%2F71695052-6ae1-49bc-b563-5dc6cad47f37%2Fz8pyrve_processed.png&w=3840&q=75)
Transcribed Image Text:The function \( f(x) = \frac{\exp(x) - \exp(-x)}{\exp(x) + \exp(-x)} + \ln(x) \) is given, where \( x \in [1, 5] \).
1. **Trapezoid Rule**: Use the trapezoid rule to approximate the integral \(\int_1^5 f(x) \, dx\).
2. **Simpson’s Rule**: Use Simpson’s rule to approximate the integral \(\int_1^5 f(x) \, dx\).
3. **Gaussian Quadrature**: Use 2 Gaussian points (\( n = 1 \)) to evaluate the integration in each sub-interval and sum them up to get the integration over the entire domain.
The interval \([1, 5]\) is divided into 4 sub-intervals using 5 nodes.
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