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Evaluate an improper integral using Jordan's Lemma

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Use residues to evaluate this improper integral

Int(from 0 to inf)[cos(ax)/(x^2+1)]dx (a>0)

(See attachment for better description.)

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Solution Summary

A step-by-step solution walks the student through the process of evaluating improper integrals using the method of residue. Jordan's Lemma is used in finding the solution. A word file is attached.

Solution Preview

First, we should determine our contour. We choose the half circle from -R to R.

So, let's look at what we need to integrate. We need to consider the piece along the x-axis from -R to R, as well as the integral around the half circle. (See attachment)

So, ...

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