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I'm studying periodic functions for Fourier series and I'm stuck in finding a function $f(t)$, periodic, such that $F(x)=\int_{0}^{x}f(t)dt$ is not periodic.

I've tried plugging $(x+t)$ as the argument for F(x), using the hypothesis that I have F(x) periodic (with period $t$, and solving an integral to know what values my function couldn't assume, but that approach didn't get me anywhere. How do I do this?

Lucas Rodrigo
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  • You could also simply choose $f(x)=1$. The key is that the integral over 1 period should not be 0, which is why lulu's example works. – Ingix Jun 21 '23 at 06:16

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