I have these two formulas from the book:

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(1) \qquad f\left(x\right) = \frac{a_0}{2}+\sum_{n=1}^\infty\left[a_n cos\left(n \Omega x\right)+b_n sin\left(n \Omega x \right)\right],

\quad \Omega = \frac{2 \pi}{T}

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[tex]

(2) \qquad b_n = \frac{2}{T} \int_{a}^{a+T} f(x) sin(n \Omega x) dx

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And I'm supposed to find the Fourier coeffecient in the following:

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(3) \qquad f(x) = 2 \delta (x-1) + \delta (x-2) = \sum_{n=1}^\infty b_n sin\left(\frac{n \pi x}{3} \right), \quad 0 \leq x \leq 3.

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Now, if I compare (3) and (1):

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sin\left(\frac{n \pi x}{3} \right) = sin(n \Omega x) \Rightarrow \Omega = \frac{\pi}{3} \Rightarrow T = 6.

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So what limits am I supposed to use for the integral, and why?

I'd appreciate any help.