how to evaluate $0$ times infinity

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I am trying to evaluate this expression (derived from integration)

$[\frac{1}{a}e^{-ax} -\frac{1}{a^2}e^{-ax}]$ between infinity and zero

I get $\frac{1}{a^2}$, but I am assuming that the first term evaluated at infinity is $0$.

Is this assumption correct, i.e. can we say $0$ times infinity $= 0$?

(Some web sites state that this is indeterminate; if so, I am not sure how to apply an "indeterminate" term to the integral).