I am evaluating the following integral:
$$\int_{-\infty}^{+\infty} a(t) exp(-i \omega t) dt,$$
with a being a function of t.
The textbook says to estimate the integral in the limits of $\omega >> 1$ and $\omega << 1$. It says that, in the limit of $\omega >> 1$, "the exponential in the integral oscillates rapidly, and the integral is small" (i.e., negligible).
I don't understand the meaning of this comment. I know that $exp(i\omega t) = cos(\omega t) + i sin(\omega t)$, but I don't get how the integral would go to zero.
Any help is appreciated!