First of all, DSP is not my expert area. I didn't take any DSP course and don't know DSP in detail but I have a question regarding Fourier Transform confusing me.
Well, suppose that we wanted to take the fourier transform of $\cos(2\pi\cdot 3x)$ and integrated over a finite interval $[-a, a]$, in that case, we would end up with an expression like this:
$$ \dfrac{\left(f-3\right)\sin\left(2{\pi}af+6{\pi}a\right)+\left(f+3\right)\sin\left(2{\pi}af-6{\pi}a\right)}{2{\pi}\cdot\left(f^2-9\right)} $$
Considering that, why cannot we obtain the exact fourier transform of $cos(2\pi\cdot 3x)$ which is $0.5 \cdot (\delta(x + 3) + \delta(x - 3))$ as we increase the integral range $[-a, a]$? How can one explain that?