Question

the fourier cosine transform of the function f(t) is​

Answer 1

SOLUTION

TO DETERMINE

The fourier cosine transform of the function f(t)

EVALUATION

Here the given function is f(t)

Now

$\displaystyle \sf{F_c(s) = \int\limits_{0}^{\infty} \: f(x) \cos sx \, dx } \: \: \: - - - - (1)$

Then

$\displaystyle \sf{ f(x)= \frac{2}{\pi} \int\limits_{0}^{\infty} \: F_c(s) \cos sx \, ds } \: \: - - - - (2)$

$\sf{Then \: function \: \: F_c(s) \: \: as \: defined \: by \: Equation \: 1 \: is \: known \: as}$

$\sf{the \: Fourier \: cosine \: transform \: of \: f(x) \: in \: \: 0 < x < \infty }$

Also the function f(x) given by Equation 2 is called inverse fourier cosine transform of $\sf{F_c(s)}$

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