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Let F(w) be the Fourier Transform of a function f(t). The F(0) is
$$\int_{-\infty}^{\infty} f(t) dt$$
$$\int_{-\infty}^{\infty} \mid {f(t)^{2}} \mid$$ dt
$$\int_{-\infty}^{\infty} \mid t.{f(t)^{2}} \mid$$ dt
$$\int_{-\infty}^{\infty} t.f(t) dt$$
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