A) Which one of the following transformations is correct when applying Gaussian quadrature to approximate the integral I = 1¹5 r² ln x dr 1. Letting z = 0.25(t+1), dx = 0.25 2. Letting z = 0.25t+1.25, dx = 0.25 3. Letting = 0.25t+2.5, dx = 0.25 4. Letting z = 1.25(t+1), dr = 1.25 5. None of the options is correct B) The two-point Gauss quadrature approximation for S¹, g(t)dt would require the evaluation of which of the following steps in the process 1. 0.25 [(0.5(0.5777350) +2.5)² In (0.5(0.5777350) +2.5) +(0.5(-0.5777350) +2.5)² ln(0.5(0.5777350) +2.5)] 2. [(0.5(0.5777350) +2.5)² In(0.5(0.5777350) +2.5) + (0.5(0.- 5777350) +2.5)² In(0.5(0.5777350) +2.5)] 3. 0.25 [(0.5(0.5777350)+2.5) In (0.5(0.5777350) +2.5) + (0.5(0.- 5777350) +2.5) In(0.5(0.5777350) +2.5)] 4. 0.25 [(0.577350)² In(0.5(0.577350) +2.5) +(-0.577350)² In (0.5(-0.577350)+2.5)] 5. None of the above options are correct
A) Which one of the following transformations is correct when applying Gaussian quadrature to approximate the integral I = 1¹5 r² ln x dr 1. Letting z = 0.25(t+1), dx = 0.25 2. Letting z = 0.25t+1.25, dx = 0.25 3. Letting = 0.25t+2.5, dx = 0.25 4. Letting z = 1.25(t+1), dr = 1.25 5. None of the options is correct B) The two-point Gauss quadrature approximation for S¹, g(t)dt would require the evaluation of which of the following steps in the process 1. 0.25 [(0.5(0.5777350) +2.5)² In (0.5(0.5777350) +2.5) +(0.5(-0.5777350) +2.5)² ln(0.5(0.5777350) +2.5)] 2. [(0.5(0.5777350) +2.5)² In(0.5(0.5777350) +2.5) + (0.5(0.- 5777350) +2.5)² In(0.5(0.5777350) +2.5)] 3. 0.25 [(0.5(0.5777350)+2.5) In (0.5(0.5777350) +2.5) + (0.5(0.- 5777350) +2.5) In(0.5(0.5777350) +2.5)] 4. 0.25 [(0.577350)² In(0.5(0.577350) +2.5) +(-0.577350)² In (0.5(-0.577350)+2.5)] 5. None of the above options are correct
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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Could you kindly assist with the following question,
Topic : Numerical Analysis
Question 17
![A)
Which one of the following transformations is correct when applying Gaussian quadrature to approximate the integral I = ₁1¹5 r² ln x dx
1. Letting a = 0.25(t+1), dx = 0.25
2.
Letting = 0.25t+1.25, dz 0.25
3. Letting x = 0.25t+2.5, dx = 0.25
4. Letting a = 1.25(t+1), dr = 1.25
5. None of the options is correct
B)
The two-point Gauss quadrature approximation for S¹, g(t)dt would require the evaluation of which of the following steps in the process
1. 0.25 [(0.5(0.5777350) +2.5)² ln(0.5(0.5777350) +2.5)
+ (0.5(-0.5777350) +2.5)² ln(0.5(0.5777350) +2.5)]
2. [(0.5(0.5777350) +2.5)² In(0.5(0.5777350) +2.5)
+ (0.5(0.- 5777350) +2.5)² ln(0.5(0.5777350) +2.5)]
3.
0.25 [(0.5(0.5777350) +2.5) In(0.5(0.5777350) +2.5)
+(0.5(0.- 5777350) +2.5) ln(0.5(0.5777350) +2.5)]
4. 0.25 [(0.577350)² In(0.5(0.577350) +2.5)
+(-0.577350)² In (0.5(-0.577350) +2.5)]
5. None of the above options are correct
Annlied Mathematics](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d4b7300-85f6-4fda-bf3b-5d34dbcdb2ca%2F8adf13e5-3c5b-47ca-951d-5e77b9a83fd6%2F0vs8qzv_processed.png&w=3840&q=75)
Transcribed Image Text:A)
Which one of the following transformations is correct when applying Gaussian quadrature to approximate the integral I = ₁1¹5 r² ln x dx
1. Letting a = 0.25(t+1), dx = 0.25
2.
Letting = 0.25t+1.25, dz 0.25
3. Letting x = 0.25t+2.5, dx = 0.25
4. Letting a = 1.25(t+1), dr = 1.25
5. None of the options is correct
B)
The two-point Gauss quadrature approximation for S¹, g(t)dt would require the evaluation of which of the following steps in the process
1. 0.25 [(0.5(0.5777350) +2.5)² ln(0.5(0.5777350) +2.5)
+ (0.5(-0.5777350) +2.5)² ln(0.5(0.5777350) +2.5)]
2. [(0.5(0.5777350) +2.5)² In(0.5(0.5777350) +2.5)
+ (0.5(0.- 5777350) +2.5)² ln(0.5(0.5777350) +2.5)]
3.
0.25 [(0.5(0.5777350) +2.5) In(0.5(0.5777350) +2.5)
+(0.5(0.- 5777350) +2.5) ln(0.5(0.5777350) +2.5)]
4. 0.25 [(0.577350)² In(0.5(0.577350) +2.5)
+(-0.577350)² In (0.5(-0.577350) +2.5)]
5. None of the above options are correct
Annlied Mathematics
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