Question

Using the identity:

L{f(t)/t}=integral F(p)dp (s -->infinity),
find the integral of:

sin(t)/t dt (0-->infinity)

Answer 1

Since L{sin t} = 1/(s^2+1)

∫[0,∞] sin(t)/t dt = ∫[0,∞] 1/(p^2+1) dp
= arctan(p) [0,∞]
= π/2