- #1

PsychonautQQ

- 784

- 11

## Homework Statement

**Wow LaTex fail... anyone know how i make this look like not ****? I had it looking all pretty on http://www.codecogs.com/latex/eqneditor.php and it gave me these codes as my latex markup but it didn't come out right... why do they look like source code and not the pretty equations they are supposed to?**

Fourier Analysis equation:

[tex]$\displaystyle v(t)=a_0 + \sum_{n=1}^N a_ncos(nwt) + \sum_{m=1}^M a_msin(mwt) [/tex]

[tex]\displaystyle a_n= \frac{2}{T}\int\limits_{\frac{-T}{2}}^{\frac{T}{2}}v\(t)cos(nwt)\, dt [/tex]

[tex]\displaystyle b_n= \frac{2}{T}\int\limits_{\frac{-T}{2}}^{\frac{T}{2}}v\(t)sin(mwt)\, dt[/tex]

To show that the coefficients a and b are given by the equations above, we multiply v(t) by cos(2∏kt/T) and integrate with respect to time from t = -T/2 to t = T/2

[tex]\displaystyle \int\limits_{\frac{-T}{2}}^{\frac{T}{2}}\ ((a_0+\sum_{n=1}^N a_n cos(\frac{2\pi nt}{T}) +\sum_{m=1}^M b_m sin(\frac{2\pi mt}{T})) [/tex]

which will give us three types of integrals

[tex]\displaystyle a_0\int\limits_{\frac{-T}{2}}^{\frac{T}{2}}cos\frac{2\pi kt}{T}\,\ dt=0[/tex]

[tex]\displaystyle \sum_{m=1}^M b_m\int\limits_{\frac{-T}{2}}^{\frac{T}{2}}sin\frac{2\pi mt}{T}cos\frac{2\pi kt}{T}dt=0[/tex]

[tex]\displaystyle \sum_{n=1}^N a_n\int\limits_{\frac{-T}{2}}^{\frac{T}{2}}cos\frac{2\pi nt}{T}cos\frac{2\pi kt}{T}dt= T/2 (n=k)[/tex]

My question is why do the first two of these three integrals equal zero?

(first time using LaTex holy crap took forever

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