Solution Found!
For each of the following integrals, specify the values of the real parameter u which
Chapter 9, Problem 9.1(choose chapter or problem)
For each of the following integrals, specify the values of the real parameter \(\sigma\) which ensure that the integral converges:
(a) \(\int_{0}^{\infty} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(b) \(\int_{-\infty}^{0} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(c) \(\int_{-5}^{5} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(d) \(\text { (d) } \int_{-\infty}^{\infty} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(e) \(\int_{-\infty}^{\infty} e^{-5|t|} e^{-(\sigma+j \omega) t} d t\)
(f) \(\int_{-\infty}^{0} e^{-5|t|} e^{-(\sigma+j \omega) t} d t\)
Questions & Answers
QUESTION:
For each of the following integrals, specify the values of the real parameter \(\sigma\) which ensure that the integral converges:
(a) \(\int_{0}^{\infty} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(b) \(\int_{-\infty}^{0} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(c) \(\int_{-5}^{5} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(d) \(\text { (d) } \int_{-\infty}^{\infty} e^{-5 t} e^{-(\sigma+j \omega) t} d t\)
(e) \(\int_{-\infty}^{\infty} e^{-5|t|} e^{-(\sigma+j \omega) t} d t\)
(f) \(\int_{-\infty}^{0} e^{-5|t|} e^{-(\sigma+j \omega) t} d t\)
Step 1 of 7
The properties of the exponent,
