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Integrals : Rayleigh's Energy Theorem (Parseval's Theorem)

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Evaluate the following integrals using Rayleigh's energy theorem (This is Parseval's theorem for Fourier transforms). All integrals spans between -∞ and ∞.

I1 = ∫ df / [α2 + (2πf)2]

I2 = ∫ sinc2(τf) df

I3 = ∫ df / [α2 + (2πf)2]2

I4 = ∫ sinc4(τf) df

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Evaluate the following integrals using Rayleigh's energy theorem (This is Parseval's theorem for Fourier transforms). All integrals spans between -∞ and ∞.

I1 = ∫ df / [α2 + (2πf)2]

I2 = ∫ sinc2(τf) df

I3 = ∫ df / [α2 + (2πf)2]2

I4 = ∫ sinc4(τf) df

You most likely have tables of Fourier pairs ...

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