Utilize, respectively, the simple Simpson's rule and Two-Point Gauss-Legendre rule to calculate the following definite integral; I = [[1I+sin(2/x)]dr Compare your numerical results with the exact solution followed and evaluate the relative errors in percentage I = 4 + cos 2 – 5 cos(2/5)+ sin(2/5)– sin 2 2 Upon your evaluation of the relative errors, which rule's result is better?
Utilize, respectively, the simple Simpson's rule and Two-Point Gauss-Legendre rule to calculate the following definite integral; I = [[1I+sin(2/x)]dr Compare your numerical results with the exact solution followed and evaluate the relative errors in percentage I = 4 + cos 2 – 5 cos(2/5)+ sin(2/5)– sin 2 2 Upon your evaluation of the relative errors, which rule's result is better?
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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Calculating the results with the appropriate method
![4).
(a) Utilize, respectively, the simple Simpson's rule and Two-Point Gauss-Legendre
rule to calculate the following definite integral;
I = [[1 + sin(2/x)]dr
%3D
(b) Compare your numerical results with the exact solution followed and evaluate the
relative errors in percentage
sin(2/5)- sin 2
I = 4+ cos 2 – V5 cos(2/5) +
2
(c) Upon your evaluation of the relative errors, which rule's result is better?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F559e1cb7-b40c-4b24-8e10-c4a16c367a61%2Fa0a33f3c-1912-4c32-a319-7d87ede99d1f%2F18kcbql_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4).
(a) Utilize, respectively, the simple Simpson's rule and Two-Point Gauss-Legendre
rule to calculate the following definite integral;
I = [[1 + sin(2/x)]dr
%3D
(b) Compare your numerical results with the exact solution followed and evaluate the
relative errors in percentage
sin(2/5)- sin 2
I = 4+ cos 2 – V5 cos(2/5) +
2
(c) Upon your evaluation of the relative errors, which rule's result is better?
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