Chapter 17, Problem 13P

(a)

To determine

Prove that the given operational transforms $F\left\{{\displaystyle {\int }_{-\infty }^{t}f\left(x\right)dx}\right\}=\frac{F\left(\omega \right)}{j\omega }$.

(b)

To determine

Explain the restriction on $f\left(x\right)$ when the result obtained in Part (a) is valid.

(c)

To determine

Explain whether the operational transform $f\left(x\right)=e^{-ax}u\left(x\right)$ is used in Part (a).