Definition:Improper Integral/Half Open Interval

Definition
Let $f$ be a real function which is continuous on the half open interval $\left[{a \,.\,.\, b}\right)$.


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

Let $f$ be a real function which is continuous on the half open interval $\left({a \,.\,.\, b}\right]$.


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