Definition:Improper Integral/Unbounded Closed Interval/Unbounded Below

Definition
Let $f$ be a real function which is continuous on the unbounded closed interval $\left({-\infty \,.\,.\, b}\right]$.

Then the improper integral of $f$ over $\left({-\infty \,.\,.\, b}\right]$ is defined as:


 * $\displaystyle \int_{\mathop \to -\infty}^b f \left({t}\right) \ \mathrm d t := \lim_{\gamma \mathop \to -\infty} \int_\gamma^b f \left({t}\right) \ \mathrm d t$