Hello, question: does the integral [tex]\int_0^\infty \frac{\sin(x)}{x^a}[/tex] converge (in the sense of Lebesgue principal value) for all [tex]a \in (0;2)[/tex]? For a=1/2, it's the Fresnel integral, but other than that, I'm not sure how to approach this.(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integrability of sin(x)*x^(-a)

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**