Show that
$$\lim_{n\to\infty} \int_1^2e^{-nx^2} dx = 0.$$
After much googling, I learned that I am working with a variation of the error function! Yay. I've never heard of it in my life and I have no idea how to show this is true.
2026-03-28 11:35:01.1774697701
Integrating variation of error function: $\int_1^2e^{-nx^2} dx$
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Since $x \mapsto e^{-nx^2}$ is decreasing over $[1,2]$, observe that $$ 0<\int_1^2e^{-nx^2} dx\leq e^{-n\times1^2}\int_1^2dx=e^{-n} $$ then let $n \to \infty$.