Show that NSK PSK\int_0^{\infty} \frac{\sin(t)}{t}dt=\frac{\pi}{2}ZSK NSK by using Laplace Transform method. I know that NSK PSKL\{\sin(t)\}=\int_0^{\infty}

diferira7c 2021-12-08 Answered
Show that
0sin(t)tdt=π2
by using Laplace Transform method. I know that
L{sin(t)}=0estsin(t)dt=1s2+1
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Expert Answer

psor32
Answered 2021-12-09 Author has 33 answers

Hint:
L(sintt)=0sinttestdt=arctan1s
EDIT: To arrive at this result, note that
I=0sinttestdt
Is=0sintestdt
=11+s2

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peterpan7117i
Answered 2021-12-10 Author has 39 answers

0sinttdt
=0e0tsinttdt
=lims0sL[sint]ds
=lims0s1s2+1ds
=lims0tan1(s)s
=lims0π2tan1(s)
=π2

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