# Contour integration to solve improper integrals

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

See attached

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#### 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 ...

#### 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.

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