Question

Find the Fourier cosine transform of f(x)= x in (0,1).​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

⇒So, the answer is $=\frac{1}{S}sin S+\frac{1}{S^2}cos S +\frac{1}{S^2}$.

Step-by-step explanation:

Fourier cosine transform,

f(x)= x in (0,1)

$F_{c}(S)= \int\limits^1_0 {f(x)} \,cos sx dx$

         $=\int\limits^1_0 {x} \, cos x dx$    

         $=xsinx+cosx+c |^1_0$

By, using Bernoulli's rule we get,

[Rule:  $\int\limits {uv} \, dx=u\int\limits {v} \, dx -u'\int\limits \int\limits \, vdxdx+u'' \int\limits \int\limits \int\limits {v} \, dx dx dx...$]

$=[\frac{xsin Sx}{S} + \frac{cos Sx}{S^{2} } ]^1_0$

$=\frac{sin S}{S} -0+\frac{cos S}{S^2} +\frac{cos 0}{S^2}$

$=\frac{1}{S}sin S+\frac{1}{S^2}cos S +\frac{1}{S^2}$

What is Fourier cosine series?

The Fourier cosine series is defined as the alternative form of the trigonometric Fourier series.

• This series is also known as polar form Fourier series or harmonic form Fourier series.
• In trigonometric Fourier series, a function x(t) contains sine and cosine terms of the same frequency.

Learn more from the links given below:

Find the Fourier Cosine transform of e^-x:-

https://brainly.in/question/27815621

The Fourier cosine transform of the function f(t) is​:-

https://brainly.in/question/34795825