Fourier transform and Parseval's Theorum

[Sarcastic_Bagel]

Consider a function F(t) which has a value of zero for negative t and, for t > 0, a value exp(-t/(2τ))

 

[Deleted member 4993]

Consider a function F(t) which has a value of zero for negative t and, for t > 0, a value exp(-t/(2τ))
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[Sarcastic_Bagel]

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this assignment

I have attempted to solve for the constants
[MATH]\frac{1}{2\pi}\int_{0}^{\infty} e^{{\frac{-t}{2 \tau}} e^{i \omega t}} dt [/MATH]Where C(ω) is the real part of the answer and S(ω) is the imaginary part.

[MATH] C(\omega) = \frac{\tau}{\pi} \frac{1}{1+(2\omega \tau)^{2}}[/MATH]
[MATH] S(\omega) = \frac{2\tau^{2}\omega}{(1+(2\omega \tau)^{2})\pi}[/MATH]Is this correct?
I don't know how to prove Parseval's theorem. Help would be much appreciated.