So I was wondering if $\int_{0}^{\infty}\sin(x^2)/x^2$is finite. My intuition is to say yes but I'm not so sure also I have no idea how to calculate the integral, so I'm looking for some tips. By the way I'm working with the Lebesgue integral.
2026-03-30 01:53:06.1774835586
Integral of $\sin(x^2)/x^2$
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Note that $\sin(x^2) < x^2$, so the integral from $0$ to $1$ is finite. Also note that the absolute value of $\frac{\sin(x^2)}{x^2}$ is at most $\frac{1}{x^2}$, the integral of which converges for $x$ from $1$ to $\infty$. So the integral is finite.