Inspired by parv mor (and M. Fourier)

Calculus Level 5

\[\large\int_{0}^{2\pi}f(t) \, dt=\int_{0}^{2\pi}f(t)\sin(t)\, dt=\int_{0}^{2\pi}f(t)\cos(t)\, dt=2\pi \]

If \(f:\mathbb{R}\rightarrow \mathbb{R}\) is a continuous function satisfying the equation (G) above, find the minimal value of \[\dfrac{1}{2\pi}\int_{0}^{2\pi}(f(t))^2\, dt .\]


Inspiration.

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