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Find the Fourier cosine transform \(f(x)=e^{-ax}\)


A) \(\Large \sqrt{\frac{2}{ \pi }} \left(\frac{a}{a^{2}+s^{2}}\right) \)

B) \(\Large \sqrt{\frac{ \pi }{2}} \left(\frac{s}{s^{2}-a^{2}}\right) \)

C) \(\Large \sqrt{\frac{2}{ \pi }} \left(\frac{s}{s^{2}-a^{2}}\right) \)

D) \(\Large \sqrt{\frac{ \pi }{2}} \left(\frac{a}{s^{2}-a^{2}}\right) \)

Correct Answer:
A) \(\Large \sqrt{\frac{2}{ \pi }} \left(\frac{a}{a^{2}+s^{2}}\right) \)

Description for Correct answer:
Ther Fourier cosine transform of

\(\Large e^{-ax}=F_{c}(e^{-ax})=\sqrt{\frac{2}{ \pi }} \left(\frac{a}{a^{2}}+s^{2}\right) \)

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