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EXERCISES
In Probs. 5-10, obtain the Fourier integral representation of the given function.
5. \( f(x)=e^{-x}, \quad-\infty<x<\infty \)
6. \( f(x)=\left\{\begin{aligned}-1, & -1<x<0 \\ 1, & 0<x<1 \\ 0, & \text { otherwise }\end{aligned}\right. \)
7. \( f(x)=\left\{\begin{array}{cc}\sin x, & |x|<\pi \\ 0, & |x|>\pi\end{array}\right. \)
8. \( f(x)=\left\{\begin{array}{cl}\sin x, & 0<x<\pi \\ 0, & \text { otherwise }\end{array}\right. \)
9. \( f(x)-\left\{\begin{array}{cc}\cos x, & 0<x<\pi \\ 0 . & \text { otherwise }\end{array}\right. \)
10. \( f(x)=e^{-x^{2}},-\infty<x<\infty \)
