Question

determine the Fourier series representation for:
f(x)=x;0≤x≤π
1; π 14 years ago

Answer 1

\[a _{n}=(1/2)\int\limits_{0}^{\pi}xcos (n \pi x / 2) dx +(1/2)\int\limits_{\pi}^{2\pi} \cos (n \pi x/2)dx\]
try to integrate that for n not equal to zero;

Answer 2

and for n=0 use
\[a _{0=}(1/2)\int\limits_{0}^{\pi}xdx +(1/2)\int\limits_{\pi}^{2\pi}dx\]

Answer 3

\[and for] n \neq0 ] use\]
\[b _{n}=(1/2)\int\limits_{0}^{\pi} xsin(n \pi x/2)+(1/2)\int\limits_{\pi}^{2\pi}\sin(n \pi x/2)\]

Answer 4

and substitute them in the fourier series form
\[f(x)=(1/2) a _{0} + \sum_{n=1}^{\infty}( a _{n} \cos(n \pi x/2) +b _{n}\sin (n \pi x/2))\]

Answer 5

have fun and good luck fazreenlyana

Answer 6

i still confused when to used the even and odd function.. n if the question does not mention about the number of N, what we should consider?? can you help me to make me clear about this situation..