panels. Evaluate I = So (a) Using a rectangular rule dr by subdividing the domain into N = {5, 10, 20, 50, 100, 200, 500, 1000}

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve for rectangular rule

Evaluate I =
=dr by subdividing the domain into N E {5, 10, 20, 50, 100, 200, 500, 1000}
panels.
(a) Using a rectangular rule
(b) Make a change of variables x = t² and use rectangular rule on new variable.
• Plot the decay of the absolute error using the above two methods.
You may obtain the exact value of the integral upto 20 digits using wolframalpha.
• Compare the two methods above in terms of accuracy and cost.
• Explain the difference in solution, if any.
• Make sure the figure has a legend and the axes are clearly marked.
Ensure that the font size for title, axes, legend are readable.
• Submit the plots obtained, entire code and the write-up.
Transcribed Image Text:Evaluate I = =dr by subdividing the domain into N E {5, 10, 20, 50, 100, 200, 500, 1000} panels. (a) Using a rectangular rule (b) Make a change of variables x = t² and use rectangular rule on new variable. • Plot the decay of the absolute error using the above two methods. You may obtain the exact value of the integral upto 20 digits using wolframalpha. • Compare the two methods above in terms of accuracy and cost. • Explain the difference in solution, if any. • Make sure the figure has a legend and the axes are clearly marked. Ensure that the font size for title, axes, legend are readable. • Submit the plots obtained, entire code and the write-up.
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