fact 1 : L { f(x) /x } = from 0 to ∞ ∫ F(s) ds
fact 2 : L{ sinx }= 1/(s^2+1)
using the above prove from 0 to ∞ ∫ sinx/x dx = π/2
please steps by steps !
L{sinx}= 1/(s^2+1)
L{ sinx/ x}=∫[s~∞] 1/(x^2+1) dx ( fact1 is wrong.)
=π/2 - arctan(s)=F(s)
∫[0~∞] (sinx)/x dx =F(0)= π/2 - arctan(0)= pi/2
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L{sinx}= 1/(s^2+1)
L{ sinx/ x}=∫[s~∞] 1/(x^2+1) dx ( fact1 is wrong.)
=π/2 - arctan(s)=F(s)
∫[0~∞] (sinx)/x dx =F(0)= π/2 - arctan(0)= pi/2