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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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