GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/22

Question 22 (Textile Engineering & Fibre Science)

A function f(x) is defined by

    \[\begin{cases}-x & \text{ for } -2\leq x<0 \\x & \text{ for } 0\leq x<2\end{cases}\]

and

    \[f(x+4)=f(x)\]

.
This periodic function f(x) with a period 4 has its Fourier series expansion as

    \[f(x)=\frac{a_0}{2}+\sum_{n=1}^{\infty}a_mcos\frac{m\pi x}{2}, a_m=\frac{1}{2}\int_{-2}^{2}f(x)cos\frac{m\pi x}{2}dx\]


The coefficient of the term cos\frac{5\pi x}{2} in the above expansion is

(A)-1
(B)-\frac{8}{5\pi}
(C)-\frac{8}{(5\pi)^2}
(D)-\frac{8}{(5\pi)^3}
[Show Answer]

Option C is correct.

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