Matematika/Furje eilutės: Skirtumas tarp puslapio versijų

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187 eilutė:
:<math>=\frac{2}{l}\left(\frac{l^2\sin\frac{n\pi l}{l}}{n\pi}+\frac{l}{n^2\pi^2}\cos\frac{n\pi x}{l}|_0^l \right)=\frac{2}{l}\left(\frac{l^2\sin(n\pi)}{n\pi}+\frac{l}{n^2\pi^2}(\cos\frac{n\pi l}{l}-\cos\frac{n\pi \cdot 0}{l}) \right)=</math>
:<math>=\frac{2}{l}\cdot \frac{l}{n^2\pi^2}(\cos(n\pi)-1) =\frac{2}{n^2\pi^2}(\cos(n\pi)-1)=\frac{2}{n^2\pi^2}((-1)^n-1)=\begin{cases}
0, \quad \text{kai} \; n \; \text{lyginis} & \\
-\frac{4l}{n^2\pi^2}, \quad \text{kai} \; n \; \text{nelyginis}. &
\end{cases}</math>