Question

Question No. 2
• Fourier cosine transform of f(x)=1
, 0<x< 1 is​

Answer 1

SOLUTION

TO DETERMINE

The Fourier cosine transform of

f(x) = 1 where 0 < x < 1

EVALUATION

Here the given function is

f(x) = 1 where 0 < x < 1

Hence the required cosine transform of f(x)

$\sf{F_c[f(x)]}$

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

$\displaystyle = \int\limits_{0}^{1} \sf{ 1. \cos sx} \: \, dx$

$\displaystyle = \int\limits_{0}^{1} \sf{ \cos sx} \: \, dx$

$= \displaystyle \sf{\left. \frac{ \sin sx}{s} \right|_0^1}$

$= \displaystyle \sf{ \frac{ \sin s}{s} - \frac{ \sin 0}{s}\: }$

$= \displaystyle \sf{ \frac{ \sin s}{s}}$

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