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DEEPTHIgv
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Homework Statement
If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is?
Answer is 1/2
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Homework Equations
the expectation value of any function g is, <g>=∫Ψ*gΨdx
The Attempt at a Solution
Here,
Ψ=f(x)
since f is independent of time
∴Ψ*=f(x)
now, for <cos 4x>=∫exp(-4x)cos(4x)exp(-4x)dx
let <cos4x>=I=∫cos(4x)exp(-8x)dx
rest of the solution if in the picture attached
my main doubt is how to put the limit infinity in sin and cos
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