(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Alpha(t) = e^(2ipit) for 0 <or= t <or= 1

Prove ABS(Integral over Alpha of [sin(x)/x^2)]dx) <or= 2epi

3. The attempt at a solution

Looking at the book I've come across what I believe I need to use to derive the relation, namely: ABS[Integral over alpha( f(x)dx)) <or= Cl(alpha) where

C >or= ABS(f(x)) for all x in the Image of alpha.

What I want to show then is that ABS(sin(x)/x^2) < C for all complex numbers with magnitude one, since alpha is just the unit circle.

My basic question is then, how can I show sin(x)/x^2 is bounded above given complex arguments?

Any help would be appreciated

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# Homework Help: Complex Integrals

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