Definition:Improper Integral/Half Open Interval/Open Above

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

Then the improper integral of $f$ over $\left[{a \,.\,.\, b}\right)$ is defined as:


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