A) -1.5 The following are results of the process of evaluating the integral I = 1¹5² In x dr analytically except 1. 1 = [mx] 1,5 -1¹52² da 2. I = 0.1923 3. T = [(x-1/3)]15 4. All of the above options are correct 5. None of the above options are correct B)
A) -1.5 The following are results of the process of evaluating the integral I = 1¹5² In x dr analytically except 1. 1 = [mx] 1,5 -1¹52² da 2. I = 0.1923 3. T = [(x-1/3)]15 4. All of the above options are correct 5. None of the above options are correct B)
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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Topic : Numerical Analysis
Question 18
![A)
The following are results of the process of evaluating the integral I = ₁1¹5 x² ln x dx analytically except
1.5
1.5
I =
= [mx] 1³ - ₁¹²5 x² dx
C)
1.
2. I 0.1923
T= [(lnx-1/3)] 15
4. All of the above options are correct
5. None of the above options are correct
3.
Which one of the following transformations is correct when applying Gaussian quadrature to approximate the integral I = ₁1¹5 r² lnx dx
= 0.25(t+1), dx = 0.25
1. Letting
2. Letting
0.25t+1.25, dx = 0.25
3. Letting
0.25t+2.5, dx = 0.25
4. Letting = 1.25(t+1), dr = 1.25
5. None of the options is correct
B)
Which of the following regarding the actual error in approximating the integral 15 ² In x de using the various numerical methods is FALSE
1.
The actual error in using the composite trapezoidal rule with h = 0.1 is 0.0014
2.
The actual error in using the basic Simpson's rule is 0.04980
3.
The actual error in using the composite Simpson's rule with n = 4 is 0.0000
4.
None of the options 1. to 3. are correct.
5. All of the options 1. to 3. are correct
When applying Gauss quadrature integration to approximate 15² In x da, the transformed integral S¹, g(t)dt is such that
1. g(t) = 0.5(0.5t +2.5)² In(0.5t +2.5) dt
2. g(t) = 0.25(0.5t + 1.25)² ln(0.5t + 1.25) dt
3. g(t) 0.25(0.5t +2.5)² ln(0.5t + 2.5) dt
4. g(t) = 0.25(0.5(t+1) ln(0.5t + 0.5) dt
5. None of the above options are correct
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Transcribed Image Text:A)
The following are results of the process of evaluating the integral I = ₁1¹5 x² ln x dx analytically except
1.5
1.5
I =
= [mx] 1³ - ₁¹²5 x² dx
C)
1.
2. I 0.1923
T= [(lnx-1/3)] 15
4. All of the above options are correct
5. None of the above options are correct
3.
Which one of the following transformations is correct when applying Gaussian quadrature to approximate the integral I = ₁1¹5 r² lnx dx
= 0.25(t+1), dx = 0.25
1. Letting
2. Letting
0.25t+1.25, dx = 0.25
3. Letting
0.25t+2.5, dx = 0.25
4. Letting = 1.25(t+1), dr = 1.25
5. None of the options is correct
B)
Which of the following regarding the actual error in approximating the integral 15 ² In x de using the various numerical methods is FALSE
1.
The actual error in using the composite trapezoidal rule with h = 0.1 is 0.0014
2.
The actual error in using the basic Simpson's rule is 0.04980
3.
The actual error in using the composite Simpson's rule with n = 4 is 0.0000
4.
None of the options 1. to 3. are correct.
5. All of the options 1. to 3. are correct
When applying Gauss quadrature integration to approximate 15² In x da, the transformed integral S¹, g(t)dt is such that
1. g(t) = 0.5(0.5t +2.5)² In(0.5t +2.5) dt
2. g(t) = 0.25(0.5t + 1.25)² ln(0.5t + 1.25) dt
3. g(t) 0.25(0.5t +2.5)² ln(0.5t + 2.5) dt
4. g(t) = 0.25(0.5(t+1) ln(0.5t + 0.5) dt
5. None of the above options are correct
D)
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