ω(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The function f(x) is defined by:

f(x) = e^2ax when x ≤ 0

0 when x > 0

Show that, for a > 0, its fourier transform may be written:

fourier transform = 1 / (2a - iω)

2. Relevant equations

fourier transform = ∫f(x)e^iωt dx

(the integral is taken over minus infinity to infinity).

3. The attempt at a solution

I think I have done the 'hard' part correct:

fourier transform = ∫e^(2ax) × e^iωt

= ∫e^(2a-iω)x

= e^(2a-iω)x / (2a-iω)x

but how would I go about getting it in the form required? Im guessing it related to the fact that the integral is taken over minus infinity to infinity - as x tends to infinity the fourier transform tends to zero.. as x tends to minus infinity.. ?? What happens to the exponent?

Also, as a side note, is what I have done so far correct? Thanks alot :)

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# Homework Help: Fourier Transforms - Tidying Up After Integration

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