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# Contour integration to solve improper integrals

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Use the contour shown (Fig. 7.11, attached) with R--> infinity to prove that

See attached

##### Solution Summary

The solution shows how to apply contour integration to solve an improper integral, in this case sin(x)/x over the entire real axis.

##### Solution Preview

We need to calculate the improper integral
(1.1)
We can rewrite the integrand:
(1.2)
And now we replace it by the complex number z:
(1.3)
And we are going to integrate over the contour:

The problem is that we have a removable singularity at the origin, which is part of the path that we want to ...

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