Definition:Improper Integral/Half Open Interval/Open Above

Definition
Let $f$ be a real function which is continuous on the half open interval $\hointr a b$.

Then the improper integral of $f$ over $\hointr a b$ is defined as:


 * $\ds \int_a^{\mathop \to b} \map f t \rd t := \lim_{\gamma \mathop \to b} \int_a^\gamma \map f t \rd t$

Also denoted as
It is common to abuse notation and write:
 * $\ds \int_a^b \map f t \rd t$

which is understood to mean exactly the same thing as $\ds \int_a^{\mathop \to b} \map f t \rd t$.