Let F(ω) be the Fourier transform of a functions f(t),

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Let F(ω) be the Fourier transform of a functions f(t), then F(0) is—

1. ∫^∞_{– ∞} f(t)dt
2. ∫^∞_{– ∞} |f(t)|²dt
3. ∫^∞_{– ∞} |tf(t)|²dt
4. ∫^∞_{– ∞} tf(t)dt

Correct Option: B

We know Fourier transform of function f(t) is given as
F(jω) = ∫^∞_{– ∞} f(t)·e^{– jωt} dt
F(0) = ∫^∞_{– ∞} f(t)·e^{– j.0.t} dt
F(0) = ∫^∞_{– ∞} f(t).dt
Hence, alternative (A) is the correct choice.