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Question 5. By considering an appropriate integral of a complex function over a contour TR in the complex plane, and the result of workshop 6, question 4, evaluate the real integral R 1 1 1 = [²₁₂²2²²₁dx = lim /^ = 2² + ₁ de I dx. + 4 R→∞ +4 R r∞ Credit will not be given for traditional real-analytic approaches to evaluating the integral using substitution and/or antiderivatives.

Question 5. By considering an appropriate integral of a complex function over a contour TR in the complex plane, and the result of workshop 6, question 4, evaluate the real integral R 1 1 1 = [²₁₂²2²²₁dx = lim /^ = 2² + ₁ de I dx. + 4 R→∞ +4 R r∞ Credit will not be given for traditional real-analytic approaches to evaluating the integral using substitution and/or antiderivatives.

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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Question 5. By considering an appropriate integral of a complex function over a contour ÃÅ in the complex plane, and the result of workshop 6, question 4, evaluate the real integral 1 x² + 4 Credit will not be given for traditional real-analytic approaches to evaluating the integral using substitution and/or antiderivatives. I= = foo R dx = lim R→∞ R 1 x² + 4 dx. A taste of things to come: this kind of problem will turn up repeatedly towards the end of the course, where we will have rather more sophisticated tools at our disposal. This one, however, we can solve now. One of the most powerful and surprising applications of complex analysis is the evaluation of real integrals, which apparently have no connection to complex numbers, via contour integration.
Transcribed Image Text:Question 5. By considering an appropriate integral of a complex function over a contour ÃÅ in the complex plane, and the result of workshop 6, question 4, evaluate the real integral 1 x² + 4 Credit will not be given for traditional real-analytic approaches to evaluating the integral using substitution and/or antiderivatives. I= = foo R dx = lim R→∞ R 1 x² + 4 dx. A taste of things to come: this kind of problem will turn up repeatedly towards the end of the course, where we will have rather more sophisticated tools at our disposal. This one, however, we can solve now. One of the most powerful and surprising applications of complex analysis is the evaluation of real integrals, which apparently have no connection to complex numbers, via contour integration.
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