Given the Fourier series in - - - for fx - x cos x- the value of a0 will be

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Engineering Mathematics

Fourier Series 2 (Sine and Cosine Series)

Given the Fou...

Question

Given the Fourier series in $(- π, π) f o r f (x) = x cos x$ , the value of $a_{0}$ will be

$- \frac{2}{3} π^{2}$

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$\frac{(- 1)^{2} 2 n}{n^{2} - 1}$

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Solution

The correct option is B 0
$f (x) = x cos x i n (- π, π)$
$∵ f (- x) = (- x) cos (- x)$
$= - x cos x = - f (x)$
so f(x) is an odd function
Now using Fourier series
$a_{0} = \frac{1}{π} \int_{- π}^{π} f (x) d x = 0$
( $∵$ f(x) is an odd)

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Given the Fourier series in (−π,π) for f(x)=xcosx, the value of a0 will be

The correct option is B 0f(x)=xcosxin(−π,π) ∵f(−x)=(−x)cos(−x) =−xcosx=−f(x) so f(x) is an odd function Now using Fourier series a0=1π∫π−πf(x)dx=0 (∵ f(x) is an odd)

Given the Fourier series in $(- π, π) f o r f (x) = x cos x$ , the value of $a_{0}$ will be

The correct option is B 0
$f (x) = x cos x i n (- π, π)$
$∵ f (- x) = (- x) cos (- x)$
$= - x cos x = - f (x)$
so f(x) is an odd function
Now using Fourier series
$a_{0} = \frac{1}{π} \int_{- π}^{π} f (x) d x = 0$
( $∵$ f(x) is an odd)