Is there any analytical way to prove that the integral [tex]\int_{2.04}^\infty \frac{\sin x}{x^2}dx[/tex] is nonegative?(adsbygoogle = window.adsbygoogle || []).push({});

I tryed to use geometrical approach, i.e. the graph of the integrand look like:

The magnitude became smaller and smaller, since [tex]\sin x[/tex] is multiplied by the decreasing function $1/x^2$, so the third area, which is positive, is bigger then the forth one, which is negative, and so on. BUT I dont know what to do with the first two areas(

OR integration by parts gave me

[tex]\int_{2.04}^\infty \frac{\sin x}{x^2}dx=\frac{\sin(2.04)}{2.04}-Ci(2.04)[/tex], where [tex]Ci(x)[/tex] is the cosine integral function.

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# Integral -- analytical way to prove this integral is non-negative?

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