Proof L[(x(t))/(t)]=int_s^(oo) X(u)du

Kayley Dickson

Kayley Dickson

Answered question

2022-11-15

Proof L [ x ( t ) t ] = s X ( u ) d u

Answer & Explanation

sellk9o

sellk9o

Beginner2022-11-16Added 11 answers

Note that e s t t = s e u t d u hence, using Fubini theorem,
0 e s t x ( t ) t d t = 0 x ( t ) ( s e u t d u ) d t = s ( 0 e u t x ( t ) d t ) d u ,
that is, considering y ( t ) = x ( t ) t and X = L x
( L y ) ( s ) = s X ( u ) d u .

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