Use the contour shown (Fig. 7.11, attached) with R--> infinity to prove that
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We need to calculate the improper integral
We can rewrite the integrand:
And now we replace it by the complex number z:
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 ...
The solution shows how to apply contour integration to solve an improper integral, in this case sin(x)/x over the entire real axis.