Question: Find the Fourier transform (mathscr{F}{f(x)}) by direct integration, where (f(x)) is given by (f(x)= begin{cases}e^{x} & text { if } x <0 0 &

Find the Fourier transform $\mathscr{F}\{f(x)\}$ by direct integration, where $f(x)$ is given by $f(x)= \begin{cases}e^{x} & \text { if } x<0 \\ 0 & \text { if } x>0\end{cases}$

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