I need to calculate this ∫∞−∞sin(z)zdz using the residue of sin(z)z.
Then I write ∫∞−∞sin(z)zdz = limR→∞Im(∫R−Reizzdz+∫CReizzdz)=2πiRes(eizz,0) where CR is the the half circunference of radius R>0 over the plane.
Then I need to show that limR→∞|∫CReizzdz|=0
Can someone help me?
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