Asked by Sara
Using the identity:
L{f(t)/t}=integral F(p)dp (s -->infinity),
find the integral of:
sin(t)/t dt (0-->infinity)
L{f(t)/t}=integral F(p)dp (s -->infinity),
find the integral of:
sin(t)/t dt (0-->infinity)
Answers
Answered by
Steve
Since L{sin t} = 1/(s^2+1)
∫[0,∞] sin(t)/t dt = ∫[0,∞] 1/(p^2+1) dp
= arctan(p) [0,∞]
= π/2
∫[0,∞] sin(t)/t dt = ∫[0,∞] 1/(p^2+1) dp
= arctan(p) [0,∞]
= π/2
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