Calculating Fourier Coefficients and Series for f(x)

[broegger]

Hi!

I have to calculate the Fourier coefficients $$c_n = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}dx$$ and the Fourier series for the following function:

$$f(x)= \begin{cases} \frac{2}{\pi}x + 2 & \text{for } x\in \left[-\pi,-\pi/2\right]\\ -\frac{2}{\pi}x & \text{for } x\in \left[-\pi/2,\pi/2\right]\\ \frac{2}{\pi}x - 2 & \text{for } x\in \left[\pi/2,\pi\right] \end{cases}$$

Since this function is odd the Fourier series should only contain $$\sin{x}$$ (right?), but I keep getting a series containing both sine and cosine. Furthermore I'm having big trouble with the integrals; are there any "tricks" when doing such integrals?

 

[TenaliRaman]

is the function really odd?
what is f(pi/2)?what is f(-pi/2)?
are they equal?

-- AI

 

[broegger]

no.. f(pi/2) = -f(pi/2) => f is odd?

 

[TenaliRaman]

Note to self : "should not study some dumb subject like software engineering, post something at physicsforums, listen to music and chat ... all at the same time"

whoops! apologies broegger!

anyways, back to ur question ...
could u post ur working ?
prolly u overlooked something ...
since u seem to have the problem well understood, u should have got the answer by now.

-- AI

 

[broegger]

nope.. I can't get the right answer.. I'd rather not post my working, since it's is very messy :/ I'm not asking someone to do the calculations; I would just like a general (the easiest) way to deal with such problems...

 

[Dr Transport]

grunt it out...no easy way to get your coefficients.