I'm stuck trying to prove a step inside a lemma from Serre; given is(adsbygoogle = window.adsbygoogle || []).push({});

0<a<b

0<x

To prove:

[tex]|\int_{a}^{b}e^{-tx}e^{-tiy}dt|\leq\int_{a}^{b}e^{-tx}dt[/tex]

I've tried using Cauchy-Schwartz for integrals, but this step is too big (using Mathematica, it lead to a contradiction); something simpler must do the trick.

Thanks in advance.

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# Inequality with absolute value of a complex integral

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