$f$ is continuous and periodic with period T. Show that $F: x \to \int_0^xf(t)dt$ can be represented as a sum of a linear and a periodic function. I have proven that $\int_x^{x+T}f(x)dx=\int_0^Tf(x)dx$, is it useful here?
2026-04-01 05:20:04.1775020804
On the structure of an integral with a variable upper limit of a continuous periodic function
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