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Integrate the following function both analytically and numerically. Use t multiple-application trapezium, and the Simpson 1/3 rule, as well as Romberg integration: sin x Use transformation of variables to eliminate the singuarity at x=0.

Integrate the following function both analytically and numerically. Use t multiple-application trapezium, and the Simpson 1/3 rule, as well as Romberg integration: sin x Use transformation of variables to eliminate the singuarity at x=0.

Advanced Engineering Mathematics
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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Integrate the following function both analytically and numerically. Use the multiple-application trapezium, and the Simpson 1/3 rule, as well as Romberg integration: S sin x -dx Use transformation of variables to eliminate the singuarity at x=0. Find the number of divisions N needed such that the relative change in the result is not larger than 10“ , when going to a larger number of steps. For each method state the number of divisions needed to reach the desired accuracy, and discuss the differences between the three methods.
Transcribed Image Text:Integrate the following function both analytically and numerically. Use the multiple-application trapezium, and the Simpson 1/3 rule, as well as Romberg integration: S sin x -dx Use transformation of variables to eliminate the singuarity at x=0. Find the number of divisions N needed such that the relative change in the result is not larger than 10“ , when going to a larger number of steps. For each method state the number of divisions needed to reach the desired accuracy, and discuss the differences between the three methods.
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