Applied Mathematics
SH 551
Question
2081 ChaitraChapter 4: Fourier Transform4.1 Fourier Integral Theorem, Fourier Sine and Cosine Integral; Complex Form of Fourier Integral
Find the Fourier cosine integral representation of $f(x)=e^{-kx}$ ($x>0$, $k>0$) and hence evaluate $\displaystyle\int_0^\infty\frac{\cos\omega x}{k^2+\omega^2},d\omega$.
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