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Residue Theorem for Evaluation

Use residue theorem to evaluate the attached.

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The solutions are explained in the attached pdf file.

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Here is the plain TEX source

centerline{bf Residue theorem}

bf 5 rm

The inregrand is bf even, rm so we can extend the integration to the whole X-axis:
$$
I = {1over 2}int_{-infty}^infty {cos 2xover 9x^2 + 4} dx
= Re l{ {1over 2}int_{-infty}^infty {e^{2ix} over 9x^2 + 4}dx r} =
$$
$$
= Re l{ {1over ...

Solution Summary

This provides several examples of using residue theorem to evaluate integrals.

$2.19