# Fourier transform

an equation involves an integration. After an inverse fourier transform of the equation, will the integration limits change? (maybe you can take a look at the attached file)

Thanks!

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CompuChip
$$F(a) = \int_0^a f(x) \, dx$$
$$\tilde F(k) = \frac{1}{\sqrt{2\pi}} \int e^{-ika} F(a) \, da = \frac{1}{\sqrt{2\pi}} \int \int_0^a f(x) e^{-ika} \, dx \, da$$