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The Laplace transform of a function f(t) defined on [0,) is defined to be, ...

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Accounting

The Laplace transform of a function f(t) defined on [0,) is defined to be,
L{f(t)}(s)=0f(t)e-stdt.
The result is a function whose domain is the set of all s values for which this improper integral
converges.
(a) Show that L{sin(t)}=1s2+1.
(b) Show that L{f(t)t}=sL{f(t)}()d.
(c) Use parts (a) and (b) to show that 0sin(t)tdt=2.
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